Emeritus Professor of Applied Mathematics 




Professor Qi Liqun
B.S, M.S, Ph.D. 

Office
Email
Telephone
Fax 
TU703, Yip Kit Chuen Bldg
maqilq@polyu.edu.hk
2766 4591
2362 9045 





Education 

 B.S. (Computational Mathematics) Tsinghua University 1968
 M.S. (Computer Sciences) University of Wisconsin 1981
 Ph.D. (Computer Sciences) University of Wisconsin 1984



Distinctions 



 ISI Most Highly Cited Scientist: http://www.isihighlycited.com/
 The First Class Science and Technology Award of Chinese Operations Research Society in 2010
 The President's Awards for Excellent Performance/Achievement 2003/2004, based upon Research and Scholarly Activities, The Hong Kong Polytechnic University
 Foreign Member of the Petrovskaya Academy of Science and Arts, Russia




Research Interests 



Optimization and Applications
 Generalized Newton Methods
 Nonlinear Programming
Multilinear Algebra
Computational Mathematics and Application
 Numerical Multilinear Algebra
 Systems of Nonlinear Equations




Research Grants 



 Chief Investigator: Tsinghua University Science Fund, 19851987
 Chief Investigator: China Science Fund, 19861987
 Chief Investigator: ARC (Australian Research Council) Grant, "The Analysis of Combinatorial and Nonsmooth Optimization and Optimal Control Problems and the Development of Computational Methods", (Womersley, Qi, Murray and Jeykumar), 19901991
 Chief Investigator: ARC Grant, "Stochastic Programming", (Qi), 19901992
 Chief Investigator: ARC Grant, "Computational Methods for Stochastic Programs with Recourse", (Qi), 1993
 Chief Investigator: ARC Grant, "Nonsmooth Equations and Nonsmooth Optimization", (Qi and Womersley), 19921995
 Chief Investigator: ARC Grant, "Stochastic Programs and Their Applications", (Qi, Womersley and TinLoi), 19951997
 Chief Investigator: ARC Grant, "Nonsmooth Optimization", (Qi and Womersley), 1996
 Chief Investigator: ARC Grant, "The Variational Inequality Problem", (Qi), 1996
 Chief Investigator: ARC Grant, "Singularity in Mathematical Programming", (Qi, Womersley and Chen), 1997
 Principal Investigator: Bilateral Science & Technology Collaboration Grant: "Superlinearly and globally convergent algorithms for minimax problem arising from engineering design", (Qi), 1997
 Chief Investigator: ARC Grant, "Generalized Newton Methods in Optimization", (Qi and Womersley), 19971999
 Chief Investigator: ARC Grant, "Smoothing and Accelerating Methods for Nonmonotone and Nondifferentiable Problems", (Qi, Chen and Fukushima), 1998
 Chief Investigator: ARC Grant, "SQP and QPfree Algorithms for Nonlinear Programming", (Qi and Womersley), 19982000
 Chief Investigator: ARC Grant, "Smoothing and NonInterior Point Methods", (Qi, Fukushima and Chen), 19992001
 Chief Investigator: ARC Grant, "Newtontype Methods for Semidefinite Problems and Constrained Approximation", (Qi, Womersley and Ye), 2000
 Projector Leader: The Hong Kong Polytechnic University Postdoctoral Fellowship Scheme, "Robust Quadratic Programming Based Methods for Variational Inequality Problems", 20002002
 Principal Investigator: RGC (The Research Grant Council of Hong Kong) Grant, "Reformulation Methods in Optimization", 20002003
 Chief Investigator: ARC (Australian Research Council) Grant, "Generalized Newton Methods for Constrained Approximation Problems and Sum of Norms", 20012003
 Projector Leader: The Hong Kong Polytechnic University Postdoctoral Fellowship Scheme, "Newtonlike Methods and Trust Region Methods", 20012003
 Chief Investigator: ARC (Australian Research Council) Discovery Grant, "Robust Reformulation Methods", 20022004
 Principal Investigator: RGC (The Research Grant Council of Hong Kong) Grant, "Robust Algorithms for Constrained Nonlinear Programs", 20012004
 Principal Investigator: RGC (The Research Grant Council of Hong Kong) Grant, "Semismooth Newton Methods for Constrained Approximation Problems", 20022005
 Projector Leader: The Hong Kong Polytechnic University Postdoctoral Fellowship Scheme, "Nonlinear Optimization: Theory, Algorithms and Applications", 20032005
 Projector Leader: The Hong Kong Polytechnic University Joint Supervision of PhD Student with Zhejiang University, "Generalized and Inverse Network Flow Problems for Manufacturing Management Systems", 20032004
 Principal Investigator: RGC (The Research Grant Council of Hong Kong) Grant, "Aggregate Reformulation Methods with Applications", 20032006
 Principal Investigator: RGC (The Research Grant Council of Hong Kong) Grant, "Multivariate Polynomial Optimization and Systems", 20042007.
 Chief Investigator: ARC Discovery Grant, "Constrained and Stable Solutions of Nonlinear and Semismooth Equations", 20052007.
 Projector Leader: The Hong Kong Polytechnic University Postdoctoral Fellowship Scheme, "Polynomial Optimization: Theory, Algorithms and Applications", 20052007.
 Principal Investigator: RGC (The Research Grant Council of Hong Kong) Grant, "Constrained and Unconstrained Nonsmooth Equation Methods", 20052008.
 Projector Leader: The Hong Kong Polytechnic University Research Funds for Recentlypromoted Chair Professors, "Solution Methods for Problems Arising from Complex Systems", 20052013.
 Projector Leader: The Hong Kong Polytechnic University Internal Grant: "AMSSPOLYU Joint Research Institute on Engineering and Management Mathematics" 20052010.
 Principal Investigator: RGC (The Research Grant Council of Hong Kong) Grant, "Eigenvalues of HigherOrder Tensors and Applications", 20072009.
 Projector Leader: The Hong Kong Polytechnic University Postdoctoral Fellowship Scheme, "Generalized Equations: Theory, Algorithms and Applications", 20072009.
 Principal Investigator: RGC (The Research Grant Council of Hong Kong) Grant, "Stable Solutions of Systems of Nonlinear Equations", 20082010.
 Principal Investigator: GRF(The Research Grant Council of Hong Kong) Grant: "Optimization Methods for Problems related with Two FourthOrder Tensors", 20092012.
 Projector Leader: The Hong Kong Polytechnic University Department of Applied Mathematics Postdoctoral Fellowship Scheme, "Diffusion Kurtosis Imaging Mathematics: Tensors Computation, Diffusion Anisotropy Indices, Simulations and Optimization'', 20082009.
 Projector Leader: The Hong Kong Polytechnic University Postdoctoral Fellowship Scheme, "Nonconvex Polynomial Optimization: Theory, Algorithms and Applications'', 20092011.
 Principal Investigator: GRF (The Research Grant Council of Hong Kong) Grant, "Computational Polynomial Optimization: Complexity and Relaxation Methods'', 20102013.
 Principal Investigator: GRF (The
Research Grant Council of Hong Kong) Grant,
"Positive semidefinite diffusion tensor
imaging and space tensor conic
programming'', 20112013.
 Projector Leader: The Hong Kong
Polytechnic University Research
Funds for Outstanding Performance in GRF
Grant Applications,
"Spectral Theory of HigherOrder Tensors'',
20112012.
 Principal Investigator: GRF (The
Research Grant Council of Hong
Kong) Grant, "Nonnegative Tensors: Theory
and Algorithms'',
20122014.
 Principal Investigator: GRF (The
Research Grant Council of Hong
Kong) Grant, "Tensor analysis: Spectral
Radius, Spectral Minimum and HProduct",
20132015.
 Principal Investigator: GRF (The
Research Grant Council of Hong
Kong) Grant, "Spectral Hypergraph
Theory via Tensor", 20142016.




Memberships 



 Member of the Physical Science Panel of
The Hong Kong
Research Grant Council (20072012)
 Member of the RGC Selection Committee
for the NSFC/RGC Joint
Research Scheme for the 2010/2011 and
2011/2012 exercises
 The Mathematical Programming Society (19861987, 19932000)
 Australian Mathematical Society (19891992)
 Hong Kong Mathematical Society (2001)




Editorial Positions 



 Editorial member, Journal of Applied Mathematics and Computational Mathematics (Shanghai) (19851988)
(2011)
 Editorial member, Journal of Tsinghua University (Natural Sciences) (19851987)
 Editorial member, Journal of Combinatorial Optimization (1995)
 Editorial member, Computational Optimization and Applications (2003)
 Editorial member, ESAIM: Control, Optimization and Calculus of Variations (20032012)
 Editor, Pacific Journal of Optimization (2003)
 Editorial member, Journal of Industrial Management and Optimization (2003)
 Editorial member, System Engineering  Theory and Practice (20082012)
 Editorial member, Frontiers of Mathematics
in China (2008)
 Editorial member, Journal of
Optimization, Theory and Applications
(2010)
 Editorial member, Optimization and
Softwares (2011)
 Guest editor for Mathematical Programming Series B: Computational Nonsmooth Optimization (1997)
 Guest editor for Journal of Computational and Applied Mathematics (2001)(2002)(2008)(2011)
 Guest editor for Computational Optimization and Application (2000)(2003)(2006)
 Guest editor for Annals of Operations Research (2001)
 Guest editor for Journal of Global Optimization (2003)(2005)
 Guest editor for Journal of Industrial Management an Optimization (2005)

Guest editor for Frontiers of Mathematics in
China (2010)

Guest editor for Numerical Linear Algebra
with Applications (2012)




Prizes and Honors 



 Championship of Mathematics Competition, Tsinghua University, 1963
 Vilas Fellowship, 1982
 Knapp Meeting Travel Fellowship, 1984
 Andrew Mellon Postdoctoral Fellowship, 19841985
 CORE Research Fellowship, 19881989
 Visiting Professor of Industrial and Operations Engineering, University of Michigan, 1995
 Visiting Professor of Applied Mathematics, Hunan University, 1996
 Visiting Professor of Mathematics, City University of Hong Kong, 1998
 Adjunct Professor of Applied Mathematics, Institute of Applied Mathematics, Chinese Academy of Sciences, 19982000
 Adjunct Professor of Mathematics, Tsinghua University, 20012004
 Research Professor of Mathematics, Curtin University of Technology, 20012004
 Visiting Professor of Mathematics, Zhongshan University, 20012005
 Adjunct Professor of Mathematics, Guangxi University, 20022006
 Adjunct Professor of Mathematics and Computer Sciences, Nanjing Normal University, 20032006
 Visiting Professor of Mathematics, University of New South Wales, 20032006
 Visiting Professor of Mathematics, Nanjing University of Aeronautics and Astronautics, 2003
 Visiting Professor of Mathematics, Changsha University of Science and Technology, 2003
 Adjunct Professor of Mathematics, Eastern China University of Science and Technology, 2003
 Associate Investigator, Australian Research Council Centre of Excellence for the Mathematics and Statistics of Complex Systems, 2004
 Visiting Professor of Mathematics, Zhejiang University, 2004
 Adjunct Professor of Mathematics, National University of Deference Technology, 2004
 Visiting Professor of Mathematics, Southeast University, 2004
 Adjunct Professor of Mathematics, Zhejiang University of Finance and Economics, 2005
 Guest Professor of Mathematics, Nankai
University, 2012
 Guest Professor of Mathematics, Tianjin
University, 20122014.
 Plenary Speaker of Second International Symposium, ISORA??6, Guilin, China, December, 1996
 Plenary Speaker of The International Conference on Nonlinear Analysis and Convex Analysis, Niigata, Japan, July, 1998
 Plenary Speaker of The International Conference on Optimization and Numerical Algebra, Nanjing, China, September, 1999
 Plenary Speaker of The Mathematical Sciences Conference for the 90th Anniversary of Tsinghua University, Beijing, China, April, 2001
 Plenary Speaker of The International Conference on Optimization and Control, Tainan, Taiwan, June, 2001
 Plenary Speaker of The International Conference on Nonlinear Analysis and Convex Analysis 2001, Hirosaki, Japan, July, 2001
 Plenary Speaker of The 4th International Symposium on Operations Research and Its Applications, YichangChongqing, China, June, 2002
 Plenary Speaker of The Second JapaneseSino Optimization Meeting, Kyoto, Japan, September, 2002
 Plenary Speaker of The MultiConference on Computational Engineering in System Applications (CESA 2003), Lille, France, July, 2003
 Plenary speaker of The International Conference on Nonlinear Analysis and Convex Analysis 2003, Tokyo, Japan, August, 2003
 Keynote speaker of The ChinaAustralia Workshop on Optimization: Theory, Methods and Applications, Shanghai, China, May, 2004
 Plenary speaker of The Eighth International on Nonlinear Functional Analysis and Applications, Masan, South Korea, August, 2004
 Keynote speaker of The Second AustraliaChina Workshop on Optimization, Ballarat, Australia, December, 2004
 Plenary speaker of The Fourth International Conference of Nonlinear Analysis
 and Convex Analysis (NACA2005), Okinawa, Japan, June, 2005.
 Plenary speaker of The First South Pacific Conference on Mathematics, Noumea, New Caledonia, August 2005.
 Plenary speaker of The Chinese Mathematical Programming Conference, Nanning, Guangxi, April, 2006.
 Plenary speaker of Joint EUROPTOMS Meeting 2007, Prague, Czech, July, 2007.
 Plenary speaker of International Symposium on Nonlinear Analysis and Convex Analysis, Kaohsiung, Taiwan, November, 2007.
 Plenary speaker of the Second International Conference on Nonlinear Programming and Applications, Beijing, China, April, 2008.
 Plenary speaker of The Fourth SinoJapanese Optimization Meeting, Tainan, Taiwan, August, 2008.
 Plenary spaker of The 100th Anniversary Memorial Meeting for Professor Zhao FangXing, Beijing, China, November, 2008.
 Plenary speaker of The Second International Conference on Numerical Algebra and Scientific Computing, Nanjing, China, November, 2008.
 Graduate School Public Lecture, Southeast University, Nanjing, China, November, 2008.
 Plenary speaker of The Third International Conference on Scientific Computing and Partial Differential Equations, Hong Kong, December, 2008.
 Plenary speaker of The 7th
International Conference on Numerical
Optimization and Numerical Linear Algebra,
Lijiang, China, August 2009.
 Plenary
speaker of The Second South Pacific
Conference on Mathematics, Noumea, New
Caledonia, August 2010.
 Plenary speaker
of The 2010 Operations Research Conference
of China, Beijing, China, October 2010.

Plenary speaker of International Conference
on Spectral Theory of Tensors, Tianjin,
China, MayJune 2012.
 Plenary speaker of
The 10th International Conference on Matrix
Theory and Its Applications, Guiyang, China,
July 2012.




Conference Organization 



 Member of the International Scientific Committee of the Fifth International Conference on Stochastic Programming, Ann Arbor, U.S.A., 1989.
 Member of the International Scientific Committee of the Sixth International Conference on Stochastic Programming, Udine, Italy, 1992.
 Member of the Scientific Computing Track Advisory Committee of the 1994, Symposium on Applied Computing, Phoenix, U.S.A., 1994.
 Member of the International Advisory Committee of the 15th International Symposium on Mathematical Programming, Ann Arbor, U.S.A., 1994.
 Member of the Scientific Computing Track Advisory Committee of the 1995, Symposium on Applied Computing, Nashiville, U.S.A., 1995.
 Member of the Scientific Computing Track Advisory Committee of the 1996, Symposium on Applied Computing, Philadelphia, U.S.A., 1996.
 Member of the International Advisory Committee of the 16th International Symposium on Mathematical Programming, Lausanne, Switzerland, 1997.
 Member of the Organization Committee of the International Conference on Numerical Optimization and Numerical Linear Algebra, Qingdao, China, 1997.
 Member of International Program Committee of the International Conference on Nonlinear Analysis and Convex Analysis, Niigata, Japan, 1998.
 Conference Chair of the International Conference on Nonlinear Programming and Variational Inequalities, Hong Kong, 1998.
 CoChair of the Organizing Committee for the First SinoJapan Optimization Meeting, Hong Kong, 2000.
 Member of the Steering Committee for the SinoJapan Optimization Meeting (2000).
 Director of the International Workshop on Optimization and Control with Applications, Erice, Italy, 2001.
 General CoChair of the 5th International Conference on Optimization: Techniques and Applications, Hong Kong, 2001.
 Director of the Second International Conference on Optimization and Control with Applications, Huangshan, China, 2002.
 Chairman of the International Scientific Committee of the 6th International Conference on Optimization: Techniques and Applications, Victoria, Australia, 2004.
 Director of the Third International Conference on Optimization and Control with Applications, hongqingChengduJiuzhaigou, China, 2004.
 Coorganizer: The International Workshop on Semiinfinite Programming, Tainan, Taiwan, August, 2005.
 Organizer: Workshop on Optimization  Dedicated to Professor M.J.D. Powell on the occasion of his 70th birthday, Hong Kong, February, 2007.
 CoDirector of Croucher Advanced Study Institute: Mathematical Algorithmic Challenge for Modelling Analysing Modern Data Sets, Hong Kong, April, 2008.
 Coorgranizer: AMSSPolyU Workshop, Hong Kong, June, 2008.
 Coorganizer: Workshop of Computational Mathematics, Hong Kong, September, 2008.
 Organizer: Workshop of Computational Polynomial Optimization and MultiLinear Algebra, December, 2008.
 CoChair: International Conference of Engineering and Computational Mathematics, Hong Kong, May, 2009.
 CoOrganizer: Workshop on Approximation
and Optimization on the Sphere and Other
Surfaces, Hong Kong, October 2009.

Organizer: Workshop on Financial Mathematics
and Applied Statistics, Hong Kong, December
2009.
 CoOrganizer: The Third
International Conference on Structured
Matrices and Tensors, Hong Kong, January
2010.
 Organizer of Workshop on
Eigenvalues of Non Negative Tensors, Hong
Kong, December 2010.
 Organizing Committee
Chairman: The International Conference on
Spectral Theory of Tensors, Tianjin, MayJune 2012.

Organizing Committee Chairman: The
International Workshop on Spectral and
Hypergraph Theory, Fuzhou, MayJune 2013.




Publications 



A. Books and Edited Volumns
 Q. Li, Z. Mo and L. Qi, Numerical Solutions of Nonlinear Systems, Science Press, Shanghai, 1987, Second Print: 1992, Third Print: 1997. (286 pages).
 D.Z. Du, L. Qi and R.S. Womersley (editors),
Recent Advances in nonsmooth Optimization,
World Scientific, New Jersey, 1995. (472 pages).
 L. Qi, A. Ruszczy?ski and R.S. Womersley (editors),
Computational Nonsmooth Optimization, Mathematical Programming Series B.
76, (NorthHolland, Amsterdam, 1997) (163 pages).
 M. Fukushima and L. Qi (editors), Reformulation  Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, Kluwer Academic Publisher, Nowell, MA. USA, 1999. (442 pages).
 M. Fukushima and L. Qi (editors), Nonsmooth and Smoothing Methods, Computational Optimization and Applications
17, (Kluwer Academic Publisher, Nowell, MA. USA, 2000. (183 pages).
 L. Qi and J. Zhang (editors), Nonlinear Programming and Variational Inequalities, Journal of Computational and Applied Mathematics
129, Elsevier Science Publisher, Amsterdam, The Netherlands, 2001. (208 pages).
 L. Qi, W. Sun and J. Zhang (editors),
Optimization and Numerical Algebra, Annals of Operations Research
103, Kluwer Academic Publisher, Nowell, MA. USA, 2001. (388 pages).
 L. Qi, X. Yang and J. Zhang (editors),
The First SinoJapan Optimization Meeting, Journal of Computational and Applied Mathematics
146, Elsevier Science Publisher, Amsterdam, The Netherlands, 2002. (177 pages).
 L. Qi (editor), A Tribute to Eljah (Lucien) Polak, Computational Optimization and Applications
25, Kluwer Academic Publisher, Nowell, MA. USA, 2003. (311 pages).
 L. Qi, K.L. Teo and X. Yang (editors),
Optimization and Control, Journal of Global Optimization
28, Kluwer Academic Publisher, Nowell, MA. USA, 2004. (100 pages).
 X. Yang, X. Yang and L. Qi (editors),
A Special Issue Dedicated to Professor Franco Giannessi on the Occasion of His 70th Birthday, Journal of Industrial Management and Optimization
1, (American Institute of Mathematical Sciences, Springfield, MO, USA, 2005). (148 pages).
 L. Qi, K.L. Teo and X. Yang (editors),
Optimization and Control with Applications, (Springer, New York, USA, 2005). (600 pages).
 D. Li, L. Qi and K.L. Teo (editors), Optimization and Control: Technology and Applications, Journal of Global Optimization
31, (Springer, New York, USA, 2005). (162 pages).
 M. Fukushima and L. Qi (editors), Special Issue for the 6th International Conference on Optimization: Technology and Applications, Computational Optimization and Applications
35, (Springer, New York, USA, 2006). (68 pages).
 M.A. Lopez, L. Qi and S.Y. Wu (editors),
SemiInfinite Programming, Journal of Computational and Applied Mathematics
217, (Elsevier Science Publisher, Amsterdam, The Netherlands, 2008).
(160 pages)
 L. Qi, L. Liao, W. Zang and
G. Zhou (editors), Continuous
Optimization and Combinatorial Optimization,
Frontiers of Mathematics in China 5,
(SpringerVerlag, New York, 2010). (190
pages)
 M. Fukushima, C.T. Kelley, L. Qi,
J. Sun and Y. Ye (editors), Special
Issue in Memory of Alexander Rubinov,
Pacific Journal of Optimization 6,
(Yokohama Publishers, Yokohama, 2010). (204
pages)  C.K. Chan, X. Chen, L. Qi, C.
Rogers. Z.C. Shi and I.H. Sloan (editors),
Engineering and Computational
Mathematics: A Special Issue of the
International Conference on Engineering and
Computational Mathematics, 27V29 May 2009,
Journal of Computational and Applied
Mathematics 235, (Elsevier Science
Publisher, Amsterdam, The Netherlands,
2011). (260 pages)
 M. Ng, R. Chan, X.
Chen, L. Qi, F. Luk and E. Tyrtyshnikov
(editors), Structured Matrices and
Tensors: A Special Issue of the Third
International Conference on Structured
Matrices and Tensors, 1922 January 2010,
Numerical Linear Algebra with Applications
19, (John Wiley & Sons, New York,
2012). (173 pages)
B. Papers in refereed Journals
 Z.T. Chi and L. Qi, "Convex functionals of lorder", Numerical Mathematics, A Journal of Chinese Universities, 1 (1979) 112119.
 Z.T. Chi and L. Qi, "Some global inverse function theorems", Numerical Mathematics, A Journal of Chinese Universities, 1 (1979) 215216.
 L. Qi, "An improved KrawczykMoore interval iteration method", Numerical Mathematics, A Journal of Chinese Universities, 2 (1980) 2634.
 L. Qi, "Solving systems of nonlinear algebraic equations with exclusion Newton methods", Numer. Comp. & Comp. Applic. 1 (1980) 109115.
 L. Qi, "Interval boxes of solutions of nonlinear systems", Computing, 27 (1981) 137144.
 L. Qi, "A note on the Moore test for nonlinear system", SIAM J. Numer. Anal. 19 (1982) 851857.
 R.E. Moore and L. Qi, "A successive interval test for nonlinear systems", SIAM J. Numer. Anal. 19 (1982) 845850.
 L. Qi, "Interval analysis", Oper. Res. (Shanghai) 1 (1982) 2935.
 L. Qi, "Uniqueness of the maximal extension of a monotone operator", Nonlinear Analysis, 7 (1983) 325332.
 L. Qi, "Complete closedness of maximal monotone operators", Mathematics of Operations Research,8 (1983) 315317.
 L. Qi, "Some simple estimates for singular values of a matrix", Linear Algebra & Its Applications, 56 (1984) 105119.
 L. Qi, "Forest iteration method for stochastic transportation problem", Mathematical Programming Study, 25 (1985) 142163.
 L. Qi, "Three pearls in mathematical programming", Nature Journal (Shanghai), 8 (1985) 299 306.
 L. Qi and A. Yin, "A discussion note on: A new numerical technique for computing surface elastic deformation caused by a given normal pressure distribution", ASME J. of Tribology, 107 (1985) 435.
 L. Qi, "An alternating method for stochastic linear programming with simple recourse", Mathematical Programming Study, 27 (1986) 182190.
 L. Qi, "The Aforest iteration method for the stochastic generalized transportation problem", Mathematics of Operations Research, 12 (1987) 121.
 L. Qi, "Total unimodularity via directed subsets", Advances in Mathematics, 16 (1987) 332.
 L. Qi, "Odd submodularity and discrete convexity", Advances in Mathematics,
16 (1987) 427429.
 L. Qi, "Odd submodular functions, Dilworth functions and discrete convex functions", Mathematics of Operations Research,
13 (1988) 435446.
 L. Qi, "Directed submodularity, ditroids and directed submodular flows", Mathematical Programming,
42 (1988) 579599.
 J.R. Birge and L. Qi, "Computing blockangular Karmarkar projections with applications to stochastic programming", Management Science ,
34 (1988) 14721479.
 L. Qi and X. Tu, "The dual forest iteration method for the stochastic transportation problem", Journal of Tsinghua Univ. , 28 (1988) 7482.
 L. Qi, "The maximal normal operator space and integration of subdifferentials of nonconvex functions", Nonlinear Analysis, 13 (1989) 10031011.
 L. Qi, "Semismoothness and decomposition of maximal normal operators", Journal of Mathematical Analysis & Applications, 146 (1990) 271279.
 L. Qi, "Quasidifferentials and maximal normal operators", Mathematical Programming,49 (1991) 263271.
 J.V. Burke and L. Qi, "Weak directional closedness and generalized subdifferentials", Journal of Mathematical Analysis & Applications, 159 (1991) 485499.
 G. Gwan and L. Qi, "On facets of the threeindex assignment polytope", Australasian Journal of Combinatorics , 6 (1992) 6787.
 J. Sun and L. Qi, "An interior point algorithm of
O?
m 7
iterations for C^{1}convex programming",
Mathematical Programming,
57 (1992) 239257.
 L. Qi, "Convergence analysis of some algorithms for solving nonsmooth equations", Mathematics of Operations Research, 18 (1993) 227244.
 L. Qi and J. Sun, "A nonsmooth version of Newton's method", Mathematical Programming, 58 (1993) 353368.
 E. Balas and L. Qi, "Lineartime separation algorithms for the threeindex assignment polytope", Discrete Applied Mathematics, 43 (1993) 112.
 J.S. Pang and L. Qi, "Nonsmooth equations: motivation and algorithms", SIAM Journal on Optimization,
3 (1993) 443465.
 J.R. Birge and L. Qi, "Semiregularity and generalized subdifferentials with applications to optimization", Mathematics of Operations Research, 18 (1993) 9821005.
 X. Chen and L. Qi, "A parameterized Newton method and a quasiNewton method for solving nonsmooth equations", Computational Optimization and Applications, 3 (1994) 157179.
 L. Qi, "Superlinearly convergent approximate Newton methods for LC^{1} optimization problems", Mathematical Programming, 64 (1994) 277294.
 L. Qi and H. Jiang, "On the range sets of variational inequalities", Journal of Optimization Theory and Applications, 83 (1994) 565585.
 L. Qi and J. Sun, "A trust region algorithm for minimization of locally Lipschitzian functions", Mathematical Programming , 66 (1994) 2543.
 L. Qi, "Trust region algorithms for solving nonsmooth equations", SIAM Journal on Optimization, 5 (1995) 219230.
 L. Qi and X. Chen, "A globally convergent successive approximation method for severely nonsmooth equations", SIAM Journal on Control and Optimization, 33 (1995) 402418.
 J.R. Birge and L. Qi, "Subdifferentials in approximation for stochastic programming", SIAM Journal on Optimization, 5 (1995) 436453.
 J.S. Pang and L. Qi, "A globally convergent Newton method for convex SC^{1} minimization problems", Journal of Optimization Theory and Applications, 85 (1995) 633648.
 R. Poliquin and L. Qi, "Iteration functions in some nonsmooth optimization algorithms" Mathematics of Operations Research, 20 (1995) 479496.
 J.R. Birge and L. Qi, "Continuous approximation schemes for solving stochastic programs", Annals of Operations Research, 56 (1995) 1538.
 L. Qi and R. Womersley, "An SQP Algorithm for extended linearquadratic problems in stochastic programming", Annals of Operations Research, 56 (1995) 251285.
 X. Chen, L. Qi, and R. Womersley, "Newton's method for quadratic stochastic programs with recourse", Journal of Computational and Applied Mathematics, 60 (1995) 2946.
 J.M. Martinez and L. Qi, "Inexact Newton methods for solving nonsmooth equations", Journal of Computational and Applied Mathematics, 60 (1995) 127145.
 H. Jiang and L. Qi, "Local Uniqueness and convergence of iterative methods for nonsmooth variational inequalities", Journal of Mathematical Analysis & Applications, 196 (1995) 314331.
 L. Qi and W. Sun, "A class of iterative methods for minimax problems", Numerical Mathematics, A Journal of Chinese Universities, Series B, 4 (1995) 237239.
 J.L. Nazareth and L. Qi, "Globalization of Newton's method for solving nonlinear equations", Journal of Numerical Algebra with Applications, 3, (1996) 239249.
 H. Jiang and L. Qi, "Globally and superlinearly convergent trust region algorithm for convex SC^{1} minimization problems and its application to stochastic programs", Journal of Optimization Theory and Applications, 90 (1996) 649670.
 Z. Wei and L. Qi, "Convergence analysis of a proximal Newton method", Numerical Functional Analysis and Optimization, 17 (1996) 463472.
 M. Fukushima and L. Qi, "A globally and superlinearly convergent algorithm for nonsmooth convex minimization", SIAM Journal on Optimization, 6 (1996) 11061120.
 L. Qi and R.S. Womersley, "On extreme singular values of matrix valued functions", Journal of Convex Analysis, 3 (1996) 153166.
 F. TinLoi, L. Qi, Z. Wei and R.S. Womersley, "Stochastic ultimate load analysis: Models and solution method", Numerical Functional Analysis and Optimization, 17 (1996) 10291043.
 H. Jiang and L. Qi, "A new nonsmooth equations approach to nonlinear complementarity problems", SIAM Journal on Control and Optimization, 35 (1997) 178193.
 L. Qi and X. Chen, "A preconditioning proximal Newton method for nondifferentiable convex optimization", Mathematical Programming, 76 (1997) 411429.
 X. Chen, Z. Nashed and L. Qi, "Convergence of Newton's method for singular smooth and nonsmooth equations using adaptive outer inverses", SIAM Journal on Optimization, 7 (1997) 445462.
 L. Qi and H. Jiang, "Semismooth KarushKuhnTucker equations and convergence analysis of Newton methods and quasiNewton methods for solving these equations", Mathematics of Operations Research, 22 (1997) 301325.
 L. Qi, "On superlinear convergence of quasiNewton methods for nonsmooth equations", Operations Research Letters , 20 (1997) 223228.
 Z. Wei, L. Qi and H. Jiang, "Some convergence properties of descent methods", Journal of Optimization Theory and Applications, 95 (1997) 177188.
 H. Jiang, M. Fukushima, L. Qi and D. Sun, "A trust region method for solving generalized complementarity problems", SIAM Journal on Optimization, 8 (1998) 140157.
 J.R. Birge, L. Qi and Z. Wei, "Convergence analysis of some methods for minimizing a nonsmooth convex function", Journal of Optimization Theory and Applications, 97 (1998) 357383.
 X. Chen, L. Qi and D. Sun, "Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities", Mathematics of Computation, 67 (1998) 519540.
 R. Mifflin, D. Sun and L. Qi, "QuasiNewton bundletype methods for nondifferentiable convex optimization", SIAM Journal on Optimization, 8 (1998) 583603.
 E. Polak and L. Qi, "A globally and superlinearly convergent scheme for minimizing a normal merit function", SIAM Journal on Control and Optimization,36 (1998) 10051019.
 Z. Wei, L. Qi and J. Birge, "A new method for nonsmooth convex optimization", Journal of Inequalities and Applications, 2 (1998) 157179.
 J.R. Birge, L. Qi and Z. Wei, "A general approach to convergence properties of some methods for nonsmooth convex optimization", Journal of Applied Mathematics and Optimization , 38 (1998) 141158.
 F. Potra, L. Qi and D. Sun, "Secant methods for semismooth equations", Numerische Mathematik, 80 (1998) 305324.
 R. Mifflin, L. Qi and D. Sun, "Properties of the MoreauYosida regularization of a piecewise C^{2} convex function", Mathematical Programming, 84 (1999) 269281.
 F. Facchinei, H. Jiang and L. Qi, "A smoothing method for mathematical programs with equilibrium constraints", Mathematical Programming, 85 (1999) 107134.
 L. Qi, "Regular pseudosmooth NCP and BVIP functions and globally and quadratically convergent generalized Newton methods for complementarity and variational inequality problems", Mathematics of Operations Research, 24 (1999) 440471.
 E. Polak, L. Qi and D. Sun, "Firstorder algorithms for generalized finite and semifinite minmax problems", Computational Optimization and Applications, 13 (1999) 137161.
 D. Sun and L. Qi, "On NCP functions", Computational Optimization and Applications, 13 (1999) 201220.
 L. Qi and D. Sun, "Improving the convergence of noninterior point algorithms for nonlinear complementarity problems", Mathematics of Computation, 69 (2000) 283304.
 L. Qi, D. Sun and G. Zhou, "A new look at smoothing Newton methods for nonlinear complementarity problems and box constrained variational inequalities", Mathematical Programming, 87 (2000) 135.
 J.R. Birge, L. Qi and Z. Wei, "A variant of the TopkinsVeinott method for solving inequality constrained optimization problems", Journal of Applied Mathematics and Optimization, 41 (2000) 309330.
 L. Qi and Z. Wei, "On the constant positive linear independence condition and its application to SQP methods", SIAM Journal on Optimization, 11 (2000) 963981.
 H. Qi and L. Qi, "A new QPfree, globally convergent, locally superlinearly convergent algorithm for inequality constrained optimization", SIAM Journal on Optimization,11 (2000) 113132.
 X. Chen, Z. Nashed and L. Qi, "Smoothing methods and semismooth methods for nondifferentiable operator equations", SIAM Journal on Numerical Analysis, 38 (2000) 12001216.
 L. Qi and G. Zhou, " A smoothing Newton method for minimizing a sum of Euclidean norms", SIAM Journal on Optimization, 11 (2000) 389410.
 L. Qi, "On an extended Lagrange claim", Journal of Optimization Theory and Applications,108 (2001) 687690.
 A.L. Dontchev, H. Qi and L. Qi, "Convergence of Newton's method for convex best interpolation", Numerische Mathematik, 87 (2001) 435456.
 D. Sun and L. Qi, "Solving variational inequality problems via smoothingnonsmooth reformulations", Journal of Computational and Applied Mathematics, 129 (2001) 3762.
 L.Z. Liao, H. Qi and L. Qi, "Solving nonlinear complementarity problems with neural networks: a reformulation method approach", Journal of Computational and Applied Mathematics, 131 (2001) 343359.
 Q. Han, L.Z. Liao, H. Qi and L. Qi, "Stability analysis of gradientbased neural networks for optimization problems", Journal of Global Optimization,19 (2001) 363381.
 E. Polak, L. Qi and D. Sun, "Secondorder algorithms for generalized finite and semiinfinite minmax problems", SIAM Journal on Optimization, 11 (2001) 937961.
 L. Qi and Z. Wei, "Corrigendum: On the constant positive linear independence condition and its application to SQP methods", SIAM Journal on Optimization, 11 (2001) 11451146.
 L. Qi and G. Zhou, "A smoothing Newton method for ball constrained variational inequalities with applications", Computing [Suppl], 15 (2001) 211225.
 L. Qi and Y. Yang, "A globally and superlinearly convergent SQP algorithm for nonlinear constrained optimization", Journal of Global Optimization, 21 (2001) 157184.
 L. Qi, D. Sun and G. Zhou, "A primaldual algorithm for minimizing a sum of Euclidean norms", Journal of Computational and Applied Mathematics, 138 (2002) 127150.
 X. Chen, L. Qi and Y. Yang, "Lagrangian globalization methods for nonlinear complementarity problems", Journal of Optimization Theory and Applications, 112 (2002) 7795.
 L. Qi and D. Sun, "Smoothing functions and smoothing Newton method for complementarity and variational inequality problems", Journal of Optimization Theory and Applications, 113 (2002) 121147.
 L. Qi and Y. Yang, "A globally and superlinearly convergent QPfree algorithm for nonlinear constrained optimization", Journal of Optimization Theory and Applications,113 (2002) 297323.
 X. Tong, D. Li and L. Qi, "An iterative method for solving semismooth equations", Journal of Computational and Applied Mathematics, 146 (2002) 110.
 L. Qi and Y. Yang, "NCP functions applied to Lagrangian globalization for the nonlinear complementarity problem", Journal of Global Optimization, 24 (2002) 261283.
 A.L. Dontchev, H. Qi, L. Qi and H. Yin, "A Newton method for shapepreserving spline interpolation", SIAM Journal on Optimization, 13 (2003) 588602.
 G. Gu, D. Li, L. Qi and S. Zhou, "Descent directions of quasiNewton methods for symmetric nonlinear equations", SIAM Journal on Numerical Analysis, 40 (2003) 17631774.
 A.L. Dontchev, H. Qi and L. Qi, "Quadratic convergence of Newton's method for convex interpolation and smoothing", Constructive Approximation, 19 (2003) 123143.
 Z. Wei, L. Qi and X. Chen, "An SQPtype method and its application in stochastic programming", Journal of Optimization Theory and Applications, 116 (2003) 205228.
 C. Kanzow, H. Qi and L. Qi, "On the minimum norm solution of linear programs", Journal of Optimization Theory and Applications, 116 (2003) 333345.
 L. Qi and H. Yin, "A strongly semismooth integral function and its application", Computational Optimization and Applications, 25 (2003) 223246.
 Y. Yang, D. Li and L. Qi, "A feasible sequential linear equation method for inequality constrained optimization",
 SIAM Journal on Optimization,13 (2003) 12221244.
 S.C. Fang and L. Qi, "Manufacturing network flows: A generalized network model for manufacturing process modelling", Optimization Methods and Software, 18 (2003) 143165.
 L. Qi and K.L. Teo, "Multivariate polynomial minimization and its application in signal processing", Journal of Global Optimization,
26 (2003) 419433.
 L. Qi, S.Y. Wu and G. Zhou, "Semismooth Newton methods for solving semiinfinite programming problems", Journal of Global Optimization, 47 (2003) 215232.
 H. Qi and L. Qi, "Finite termination of a dual Newton method for convex best C^{1} interpolation and smoothing", Numerische Mathematik 96 (2003) 317337.
 H. Qi, L. Qi and D. Sun, "Solving KKT systems via the trust region and the conjugate gradient methods", SIAM Journal on Optimization 14 (2004) 439463.
 L. Qi, X. Tong and D. Li, "An activeset projected trust region algorithm for box constrained nonsmooth equations", Journal of Optimization Theory and Applications 120 (2004) 601625.
 Y. Wang, H. Yin and L. Qi, "NoArbitrage interpolation of the option price function and its reformulation", Journal of Optimization Theory and Applications 120 (2004) 627649.
 H. Qi and L. Qi, "Deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis", IEEE Transactions on Neural Networks 15 (2004) 99109.
 L.Z. Liao, H. Qi and L. Qi, "Neurodynamical optimization", Journal of Global Optimization 28 (2004) 175195.
 J. Sun, D. Sun and L. Qi, "A squared smoothing Newton method for nonsmooth matrix equations and its applications in semidefinite optimization problems", SIAM Journal on Optimization 14 (2004) 783806.
 D. Li, M. Fukushima, L. Qi and N. Yamashita, "Regularized Newton methods for convex minimization problems with singular solutions", Computational Optimization and Applications 28 (2004) 131147.
 Z. Huang, L. Qi and D. Sun, "Subquadratic convergence of a smoothing Newton algorithm for the P0 and monotone LCP", Mathematical Programming 99 (2004) 423441.
 X. Tong and L. Qi, "On the convergence of a trust region method for solving constrained nonlinear equations with degenerate solutions", Journal of Optimization Theory and Applications 123 (2004) 187212.
 D. Li, L. Qi, J. Tam and S.Y. Wu, "A smoothing Newton method for semiinfinite programming", Journal of Global Optimization 30 (2004) 169194.
 X. Chen, H. Qi, L. Qi and K.L. Teo, "Smooth convex approximation to the maximum eigenvalue function", Journal of Global Optimization 30 (2004) 253270.
 L. Qi, "Extrema of a real polynomial", Journal of Global Optimization 30 (2004) 405433.
 Y. Yang and L. Qi, "Smoothing trust region methods for nonlinear complementarity problems with P0 functions", Annals of Operations Research 133 (2005) 99117.
 C. Ling, X. Chen, M. Fukushima and L. Qi, "A smoothing implicit programming approach for solving a class of stochastic generalized semiinfinite programming problems", Pacific Journal of Optimization 1 (2005) 127145.
 J. Mo, L. Qi and Z. Wei, "A network simplex algorithm for simple manufacturing network model", Journal of Industrial Management and Optimization 1 (2005) 251273.
 L. Qi, Z. Wan and Y. Yang, "Global minimization of normal quartic polynomials based on global descent directions", SIAM Journal on Optimization 15 (2005) 275302.
 L. Qi, A. Shapiro and C. Ling, "Differentiability and semismoothness properties of integral functions and their applications", Mathematical Programming 102 (2005) 223248.
 F. Wang and L. Qi, "Comments on 'Explicit criterion for the positive definiteness of a general quartic form' ", IEEE Transactions on Automatic Control 50 (2005) 416 418.
 L.Z. Liao, L. Qi and H.W. Tam, "A gradientbased continuous method for largescale optimization problems", Journal of Global Optimization 31 (2005) 271286.
 L. Qi, "Eigenvalues of a real supersymmetric tensor", Journal of Symbolic Computation 40 (2005) 13021324.
 X.B. Gao, L.Z. Liao and L. Qi, "A novel neural network for variational inequalities with linear and nonlinear constraints", IEEE Transactions on Neural Networks 16 (2005) 13051317.
 H. Qi, L. Qi and X. Yang, "Deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis II", IEEE Transactions on Neural Networks 16 (2005) 17011706.
 J. Mo, L. Qi and Z. Wei, "A manufacturing supply chain optimization model for distilling process", Applied Mathematics and Computation 171 (2005) 464485.
 S.Y. Wu, D. Li, L. Qi and G. Zhou, "An iterative method for solving KKT system of the semiinfinite programming", Optimization Methods and Software 20 (2005) 629643.
 Y. Wang, X. Zhang and L. Qi, "Unconstrained optimization reformulation of the generalized complementarity problem and related method", Optimization 54 (2005) 563577.
 X. Tong, L. Qi and Y. Yang, "The Lagrangian globalization method for nonsmooth constrained equations", Computational Optimization and Applications 33 (2006) 89109.
 Q. Ni, C. Ling, L. Qi and K.L. Teo, "A truncated projected Newtontype algorithm for large scale semiinfinite programming", SIAM Journal on Optimization 16 (2006) 11371154.
 H. Yin, C. Ling and L. Qi, "Convergence rate of Newton's method for L2 spectral estimation", Mathematical Programming 107 (2006) 539546.
 L. Qi, "Boundedness and regularity properties of semismooth reformulations of variational inequalities", Journal of Global Optimization 35 (2006) 343366.
 H. Lu, E. Yao and L. Qi, "Some further results on minimum distribution cost flow problems", Journal of Combinatorial Optimization 11 (2006) 351371.
 Z. Wei, G. Li and L. Qi, "New quasiNewton methods for unconstrained optimization problems", Applied Mathematics and Computation 175 (2006) 11561188.
 Z. Wei, G. Li and L. Qi, "New nonlinear conjugate gradient formulas for largescale unconstrained optimization problems", Applied Mathematics and Computation 179 (2006) 407430.
 G. Zhou and L. Qi, "On the convergence of an inexact Newtontype method", Operations Research Letters 34 (2006) 647652.
 B. Zhang, J. Zhang and L. Qi, "The shortest path improvement problems under Hamming distance", Journal of Combinatorial Optimization 12 (2006) 351361.
 C. Ling, L. Qi, G. Zhou and S.Y. Wu, "Global convergence of a robust smoothing SQP method for semiinfinite programming", Journal of Optimization Theory and Applications 129 (2006) 147164.
 L. Qi, "Rank and eigenvalues of a supersymmetric tensor, the multivariate homogeneous polynomial and the algebraic hypersurface it defines", Journal of Symbolic Computation 41 (2006) 13091327.
 L. Qi, "Eigenvalues and invariants of tensors", Journal of Mathematical Analysis & Applications 325 (2007) 13631377.
 G. Ni, L. Qi, F. Wang and Y. Wang, "The degree of the Echaracteristic polynomial of an even order tensor", Journal of Mathematical Analysis & Applications 329 (2007) 12181229.
 L. Qi and P. Tseng, "On almost smooth functions and piecewise smooth functions", Nonlinear Analysis 67 (2007) 773794.
 X. Tong, F. Wu and L. Qi, "On the convergence of decoupled optimal power flow methods", Numerical Functional Analysis and Optimization 28 (2007) 467485.
 Y. Wang and L. Qi, "On the Successive Supersymmetric Rank1 Decomposition of Higher Order Supersymmetric Tensors", Numerical Linear Algebra with Applications 14 (2007) 503519.
 M.K. Ng, L. Qi, Y.F. Yang and Y. Huang, "On semismooth Newton's methods for total variation minimization", Journal of Mathematical Imaging and Vision
27 (2007) 265276.
 L. Qi, W. Sun and Y. Wang, "Numerical multilinear algebra and its applications",
Frontiers of Mathematics in China 2 (2007) 501526.
 X. Tong, F.F.Wu and L. Qi, Available transfer capability calculation using a smoothing pointwise maximum function??
IEEE Transactions on Circuits and Systems I 55 (2008) 462474.
 L. Qi. Z. Yan and H. Yin, Semismooth reformulation and Newtons method for the security region problem of power systems??
Journal of Industrial and Management Optimization 4 (2008) 143154.
 D. Li, L. Qi and V. Roshchina, A new class of quasiNewton updating formulas??
Optimization and Software 23 (2008) 237249.
 X. Tong, C. Ling and L. Qi, A
semiinfinite programming algorithm for
solving optimal flow with transient
stability constraints?? Journal of
Computational and Applied Mathematics 217(2008) 432447.
 C. Ling, L. Qi, G. Zhou, L. Caccetta, The SC1 Properties of an expected residual function arising from stochastic complementarity problems??
Operations Research Letters 36 (2008) 456460.
 H. Yin, Z. Huang and L. Qi, The convergence of a LevenbergMarquardt Method for the least l 2norm solution of inconsistent nonlinear inequalities??
Numerical Functional Analysis and Optimization 29 (2008) 687716.
 E.S. Hui, M.M. Cheung, L. Qi and E.X. Wu, Towards better MR characterization of neural tissues using directional diffusion kurtosis analysis??
Neuroimage 42 (2008) 122134.
 Z. Wei, G. Li and L. Qi, Global convergence of the PolakRibierePolyak conjugate gradient methods with inexact line searches for nonconvex unconstrained optimization problems??
Mathematics of Computation 77 (2008) 21732193.
 Q. Ni, L. Qi and F. Wang, An eigenvalue method for the positive definiteness identification problem??
IEEE Transactions on Automatic Control 53 (2008) 10961107.
 L. Qi, Y. Wang and E.X. Wu, Deigenvalues of diffusion kurtosis tensors??
Journal of Computational and Applied Mathematics 221 (2008) 150157.
 D. Han, L. Qi and E.X. Wu, Extreme diffusion values for nonGaussian diffusions??
Optimization and Software 23 (2008) 703716.
 C.T. Kelley, L.Z. Liao, L. Qi, M.T. Chu, J.R. Reese and C. Winton, Projected Pseudotransient continuation??
SIAM J. on Numerical Analysis 46 (2008) 30713083.
 L. Qi, C. Ling, X. Tong and G. Zhou, A smoothing projected Newtontype algorithm for semiinfinite programming??
Computational Optimization and Applications 42 (2009) 130.
 L. Qi, D. Han and E.X. Wu, Principal invariants and inherent parameters of diffusion kurtosis tensors??
Journal of Mathematical Analysis & Applications 349 (2009) 165 180.
 L. Qi, F. Wang and Y. Wang, Zeigenvalue methods for a global polynomial optimization problem??
Mathematical Programming 118 (2009) 301316.
 M.M Cheung, E.S Hui, K.C Chan, J.A Helpern, L. Qi and E.X. Wu, "Does diffusion kurtosis imaging lead to better neural tissue characterization? A rodent brain maturation study'',
Neuroimage 45 (2009) 386392.
 L. Qi, H.H. Dai and D. Han. "Conditions for strong ellipticity and Meigenvalues'',
Frontiers of Mathematics in China 4 (2009) 349364.
 H. Yin, Y. Wang and L. Qi, "Shapepreserving interpolation and smoothing for option market implied volatility'',
Journal of Optimization Theory and Applications 142 (2009) 243266.
 G. Yu, L. Qi and Y. Dai, "On nonmonotone Chambolle gradient projection algorithms for total variation image restoration'',
Journal of Mathematical Imaging and Vision 35 (2009) 143154.
 H. Sun, Y. Wang and L. Qi, "Global error bound for the generalized linear complementarity problem over a polyhedral cone'',
Journal of Optimization Theory and Applications 142 (2009) 417429.
 Y. Wang, L. Qi and X. Zhang, "A practical method for computing the largest Meigenvalue of a fourthorder partially symmetric tensor'',
Numerical Linear Algebra with Applications 16 (2009) 589601.
 D. Han, H.H. Dai and L. Qi, "Conditions
for strong ellipticity of anisotropic
elastic materials'', Journal of Elasticity
97 (2009) 113.
 C. Ling, J. Nie, L. Qi and Y. Ye,
"Biquadratic optimization over unit spheres
and semidefinite programming relaxations'',
SIAM Journal on Optimization 20
(2009) 12861310.
 M. Ng, L. Qi and G. Zhou, "Finding the
largest eigenvalue of a nonnegative
tensor'', SIAM Journal on Matrix Analysis
and Applications 31 (2009) 10901099.
 L. Qi, X. Tong and Y. Wang, "Computing
power system parameters to maximize the
small signal stability margin based on
minmax models'', Optimization and
Engineering 10 (2009) 465476.
 X. Tong, F. Wu and L. Qi, "WorstCase
CVaR based portfolio optimization models
with applications to scenario planning'',
Optimization Methods and Software
24 (2009)
933958.
 Z.J. Bai, M. Ng and L. Qi, "A
coordinate gradient descent method for
nonsmooth nonseparable minimization'',
Numerical Mathematics: Theory, Methods and
Applications 2 (2009) 155174.
 J. Chen and L. Qi, "Globally and
superlinearly convergent inexact
NewtonKrylov algorithms for solving
nonsmooth equations', Numerical Linear
Algebra with Applications 17 (2010)
155174.
 M.A. Lopez, S.Y. Wu, C. Ling and L. Qi,
"A mathematical programming approach to
strong separation in normed spaces'',
Journal of Convex Analysis 17 (2010)
211227.
 C. Ling, Q. Ni, L. Qi and S. Wu, "A new
smoothing Newtontype algorithm for
semiinfinite programming'', Journal
of Global Optimization 47 (2010)
133159.
 X. Tong, L. Qi, F. Wu and H. Zhou, "A
smoothing method for solving portfolio
optimization with CVaR and applications in
allocation of generation asset'',
Applied Mathematics and Computation 216
(2010) 17231740.
 X. Zhang, C. Ling, L. Qi and E.X. Wu
"The measure of diffusion skewness and
kurtosis in magnetic resonance imaging'',
Pacific Journal of Optimization 6
(2010) 391404.
 K.C. Chang, L. Qi and G. Zhou,
"Singular values of a real rectangular
tensor'', Journal of Mathematical
Analysis & Applications 370 (2010)
284294.
 G. Yu, L. Qi, Y. Sun and Y. Zhou,
"Impulse noise removal by a nonmonotone
adaptive gradient method'', Signal
Processing 90 (2010) 28912897.
 F. Wang, D. Li and L. Qi, "Global
convergence of GaussNewtonMBFGS method for
solving the nonlinear least squares
problem'', Advanced Modeling and
Optimization 12 (2010) 119.
 L. Qi, G. Yu and E.X. Wu, "Higher order
positive semidefinite diffusion tensor
imaging'', SIAM Journal on Imaging
Sciences 3 (2010) 416433.
 J. Chen and L. Qi, "Pseudotransient
continuation for solving systems of
nonsmooth equations with inequality
constraints'', Journal of Optimization
Theory and Applications 147
(2010) 223242.
 Z. Yang, W. Sun and L. Qi, "Global
convergence of
filtertrustregion algorithm for solving
nonsmooth equations'',
International Journal of Computer Mathematics 87 (2010)
788796.
 Y. Zhang, W. Sun and L. Qi, "A
nonmonotone globalization algorithm with
preconditioned gradient path for
unconstrained optimization'',
AsiaPacific Journal of
Operations Research 27 (2010)
5569.
 Q. Zhou, W. Sun and L. Qi, "A
nonmonotone filter BarzilaiBorwein Method
for optimization'', Applied
Mathematics and Computation 217
(2010) 42574267.
 X. Zhang, C. Ling and L. Qi, "Semidefinite
relaxation bounds for biquadratic
optimization problems with quadratic
constraints'', Journal of Global
Optimization 49 (2011) 293311.
 C.T. Kelley, L. Qi, X. Tong and H. Yin,
"Finding a stable solution of a system of
nonlinear equations'', Journal of
Industrial and Management Optimization
7 (2011) 497521.
 C. Ling, L. Qi, G. Zhou and L. Caccetta,
"Properties of expected residual functions
arising from stochastic complementarity
problems'', Pacific Journal of
Optimization 7 (2011) 249262.
 L. Qi, "The Best RankOne Approximation
Ratio of a Tensor Space'', SIAM
Journal on Matrix Analysis and Applications
32 (2011) 430432.
 C. Ling and L. Qi, "Some results
on l^{k}eigenvalues of tensor and related
spectral radius", Numerical Algebra,
Control and Optimization 1 (2011)
381388.
 Y. Xu, W. Sun and L. Qi, "A feasible
direction method for semidefinite program
with box constraints", Applied
Mathematics Letters 24 (2011)
18741881.
 Y. Chen, D. Han and L. Qi, "New ALS
methods with extrapolating search directions
and optimal step size for complexvalued
tensor decompositions", IEEE Transactions
on Signal Processing 59 (2011)
58885897.
 L. Zhang, L. Qi and Y. Xu,
"Linear convergence of the LZI algorithm for
weakly positive tensors", Journal of
Computational Mathematics 30
(2012) 2433.
 X. Tong, L. Qi, S.Y. Wu and F.F. Wu, "A
smoothing SQP method for nonlinear programs
with stability constraints arising from
power systems", Computational
Optimization and Applications 51
(2012) 175197.
 C. Ling, X. Zhang and L. Qi, "Semidefinite
relaxation approximation for multivariate
biquadratic optimization with quadratic
constraints", Numerical Linear Algebra
with Applications 19 (2012)
113131.
 S.L. Hu, Z.H. Huang, H.Y. Ni and L. Qi,
"Positive definiteness of diffusion kurtosis
imaging", Inverse Problems and Imaging
6 (2012) 5775.
 I.M. Bomze, C. Ling, L. Qi and X.
Zhang, "Standard biquadratic optimization
problems and unconstrained polynomial
reformulations", Journal of Global
Optimization 52 (2012) 663687.
 H. Yin, C. Ling and L. Qi, "Smooth and
semismooth Newton methods for constrained
approximation and estimation", Numerical
Functional Analysis and Optimization
33 (2012) 558V589.
 X. Zhang, L. Qi and Y. Ye, "The cubic
spherical optimization problems",
Mathematics of Computation 81
(2012), 15131525.
 Y. Song and L. Qi, "The existence and
uniqueness of eigenvalue for monotone
homogeneous mapping pairs", Nonlinear
Analysis 75 (2012) 52835293.
 X. Zhang, C. Ling and L. Qi, "The best
rank1 approximation of a symmetric tensor
and related spherical optimization
problems", SIAM Journal on Matrix
Analysis and Applications 33
(2012) 806821.

S. Hu and L. Qi,
"Algebraic connectivity of an even uniform
hypergraph",
Journal of Combinatorial Optimization
24
(2012) 564579.

L.
Zhang and L. Qi, "Linear convergence of an
algorithm for computing the largest
eigenvalue of a nonnegative tensor",
Numerical Linear Algebra with Applications
19
(2012) 830841.

A.M. Li, L. Qi and B. Zhang,
"Echaracteristic polynomials of tensors",
Communications in Mathematical Sciences
11 (2013) 3353.

G. Li, L. Qi and
G. Yu, "Semismoothness of the maximum
eigenvalue function of a symmetric tensor
and its application",
Linear Algebra and Its Applications
438
(2013) 813833.

G. Zhou, L.
Caccetta and L. Qi, "Convergence of an
algorithm for the largest singular value of
a nonnegative rectangular tensor", Linear
Algebra and Its Applications 438
(2013) 959968.

S. Hu and L. Qi,
"Echaracteristic polynomial of a tensor of
dimension two'',
Applied Mathematics Letters
26
(2013) 225231.

S. Hu, Z. Huang,
C. Ling and L. Qi, "On Determinants and
Eigenvalue Theory of Tensors'',
Journal of Symbolic Computation
50
(2013) 508531.

C. Ling and L. Qi,
"On Ɩ^{ k,s}singular values and
spectral radius of rectangular tensors'',
Frontiers of Mathematics in China
8
(2013) 6384.

G. Zhou, L. Qi
and S.Y. Wu, "Efficient algorithms for
computing the largest eigenvalue of a
nonnegative tensor",
Frontiers of Mathematics in China
8
(2013) 155168.

L. Qi, G. Yu and
Y. Xu, "Nonnegative diffusion orientation
distribution function'',
Journal of Mathematical
Imaging and Vision
45
(2013) 103113.

L. Qi, Y. Xu, Y.
Yuan and X. Zhang, "A cone constrained
convex program: structure and algorithms'',
Journal of
Operations Research Society of China
1
(2013) 3753.

L. Qi, "Symmetric
nonnegative tensors and copositive
tensors'',
Linear Algebra and Its Applications
439
(2013) 228238.

Y. Song and L. Qi,
"Positive eigenvalueeigenvector of
nonlinear positive mappings'', to appear in:
Frontiers of Mathematics in China.

D. Han and L. Qi,
"A successive approximation method for
quantum separability'', to appear in:
Frontiers of
Mathematics in China.

G. Li, L. Qi and
G. Yu, "The Zeigenvalues of a symmetric
tensor and its application to spectral
hypergraph theory'', to appear in:
Numerical Linear Algebra with Applications.

S. Hu and L. Qi,
"The Laplacian of a uniform hypergraph'', to
appear in:
Journal of Combinatorial
Optimization.

L. Zhang, L. Qi,
Z. Luo and Y. Xu, "The dominant eigenvalue
of an essentially nonnegative tensor'', to
appear in:
Numerical Linear Algebra with Applications.

S. Hu, G. Li, L.
Qi and Y. Song, "Finding the maximum
eigenvalue of essentially nonnegative
symmetric tensors via sum of squares
programming on the largest eigenvalue of a
symmetric nonnegative tensor'', to appear
in:
Journal of Optimization Theory and
Applications.

G. Zhou, L. Qi
and S.Y. Wu, "On the largest eigenvalue of a
symmetric nonnegative tensor'', to appear
in:
Numerical Linear Algebra with Applications.

L. Qi, Z. Wei and
G. Yuan, "An activeset projected trust
region algorithm with limited memory BFGS
technique for boxconstrained nonsmooth
equations'', to appear in:
Optimization.

S. Hu, Z. Huang
and L. Qi, "Finding the Extreme ZEigenvalues
of Tensors via a Sequential SDPs Method'',
to appear in:
Numerical Linear Algebra with Applications.

Y. Xu, W. Sun and
L. Qi, "On solving a class of linear
semiinfinite programming by SDP method'',
to appear in:
Optimization.

L. Qi and Y. Ye,
``Space tensor conic programming'', to
appear in:
Computational Optimization and Applications.

L. Qi, "Hplus
eigenvalues of Laplacian and signless
Laplacian tensors'',
Communications in Mathematical Sciences.

S. Hu, Z. Huang
and L. Qi, "Strictly nonnegative tensors and
nonnegative tensor partition'', to appear
in:
Science China Mathematics.

S. Hu and L. Qi,
"The Eeigenvectors of tensors'', to appear
in:
Linear and Multilinear Algebra.
C. Papers in Edited Books
 L. Qi, "A generalization of the KrawczykMoore Algorithm", in: Interval Mathematics 1980, K. Nickel ed. (Academic Press, New York, 1981) 481488.
 J. Sun, K.H. Tsai and L. Qi, "A simplex method for network programs with convex separable piecewise linear costs and its application to stochastic transshipment problems", in: Network Optimization Problems: Algorithms, Applications and Complexity, D.Z. Du and P.M. Pardalos eds., (World Scientific Publishing Co., London, 1993) 283300.
 L. Qi, E. Balas and G. Gwan, "A new facet class and a polyhedral method for the threeindex assignment problem", in: New Advances in Optimization and Approximation, D.Z. Du and J. Sun eds., (Kluwer Academic Publisher, Nowell, MA. USA, 1994) 256274.
 L. Qi and W. Sun, "An iterative method for the minimax problem", in: Minimax and Applications, D.Z. Du and P.M. Pardalos eds., (Kluwer Academic Publisher, Nowell, MA. USA, 1995) 5567.
 H. Jiang, L. Qi, X. Chen and D. Sun, "Semismoothness and superlinear convergence in nonsmooth optimization and nonsmooth equations", invited paper, Nonlinear Optimization and Applications, G. Di Pillo and F. Giannessi eds., (Plenum Publishing Corporation, New York, 1996) 197212.
 L. Qi, "LC^{1} functions and LC^{1} optimization", invited paper, Operations Research and Its Application, D.Z. Du, X.S. Zhang and K. Cheng eds., (World Publishing, Beijing, 1996) 413.
 D. Sun, M. Fukushima and L. Qi, "A computable generalized Hessian of the Dgap function and Newtontype methods for variational inequality problem", Complementarity and Variational Problems:  State of the Art, M.C. Ferris and J.S. Pang, eds., (SIAM Publications, Philadelphia, 1997) 452473.
 G. Zhou, D. Sun and L. Qi, "Numerical experiments for a class of squared smoothing Newton methods for complementarity and variational inequality problems", Reformulation  Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, M. Fukushima and L. Qi, eds., (Kluwer Academic Publisher, Nowell, MA. USA, 1999) 421442.
 L. Qi, "SecondOrder Analysis of the MoreauYoshida Regularization", Nonlinear Analysis and Convex Analysis, W. Takahashi and T. Tanaka, eds., (World Scientific Publishing Co., London, 1999) 1625.
 L. Qi and D. Sun, "Nonsmooth equations and smoothing methods", Progress in Optimization: Contributions from Australasia, A. Eberhard, B. Glover, R. Hill and D. Ralph, eds., (Kluwer Academic Publisher, Nowell, MA. USA, 1999) 121146.
 L. Qi, D. Ralph and G. Zhou, "Semiderivative functions and reformulation methods for solving complementarity and variational inequality problems", Nonlinear Optimization and Related Topics, G. Di Pillo and F. Giannessi, eds., (Kluwer Academic Publisher, Nowell, MA. USA, 2000) 317350.
 J.R. Birge, S.M. Pollock and L. Qi, "A quadratic recourse function for the twostage stochastic program", Progress II in Optimization: Contributions from Australasia, X.Q. Yang, A.I. Mees, M.E. Fisher and L.S. Jennings eds., (Kluwer Academic Publisher, Nowell, MA. USA, 2000) 109121.
 L. Qi and D. Sun, "Polyhedral methods for solving three index assignment problems", Nonlinear Assignment Problems: Algorithms and Applications, P.M. Pardalos and L. Pitsoulis, eds., (Kluwer Academic Publisher, Nowell, MA. USA, 2000) 91107.
 L. Qi and D. Sun, "Nonsmooth and smoothing methods for NCP and VI", Encyclopedia of Optimization, C.A. Floudas and P.M. Pardalos, eds., (Kluwer Academic Publisher, Nowell, MA. USA, 2001) 100104.
 A.L. Dontchev, H. Qi and L. Qi, "Quadratic convergence of Newton's method for constrained interpolation", Approximation Theory X: Wavelets, Splines and Applications, C.K. Chui, L.L. Schumaker and J. Stoeckler, eds., (Vanderbilt University Press, Nashville, TN, USA, 2002) 261270.
 L. Qi, "Shapepreserving interpolation, semismooth Newton methods and the option price problem", Operations Research and Its Applications, X.S. Zhang and D. Liu, eds., (World Publishing, Beijing, 2002) 6780.
 L. Qi, "Semismoothness properties and applications of an integral function", Proceedings of The Fourteenth RAMP Symposium, A. Tamura and H. Ito, eds., (RAMP, Kyoto, 2002) 103114.
 L. Qi and P. Tseng, "Almost smooth functions", Nonlinear Analysis and Convex Analysis 2001, W. Takahashi and T. Tanaka, eds., (Yokohama Publishing Co., Tokyo, 2003) 405413.
 E. Polak and L. Qi, "Some optimality conditions for minimax problems and nonlinear programs", in Numerical Linear Algebra and Optimization, Proceedings of the 2003's International Conference on Numerical Optimization and Numerical Linear Algebra, Y.X. Yuan, ed., (Science Press, Beijing, China, 2004), 4255.
 L. Qi, "Semismooth Newton methods for shapepreserving interpolation, option price and semiinfinite programs", Variational Analysis and Applications, F. Giannessi and A. Maugeri, eds., (Kluwer Academic Publisher, Nowell, MA. USA, 2005) 905919.
 L. Qi and J. Zhang, "A lexicographic classification of plane algebraic curves", Nonlinear Analysis and Convex Analysis 2005, W. Takahashi and T. Tanaka, eds., (Yokohama Publishing Co., Tokyo, 2007) 527544.
 E.S. Hui, M.M. Cheung, L. Qi and E.X. Wu, "Advanced MR diffusion characterization of neural tissue using directional diffusion kurtosis analysis'', Conf. Proc. IEEE Eng. Med. Biol. Soc. 2008 (2008) 39413944.
D. Technical reports and Manuscripts
 L. Qi, "An interval test using the new Krawczyk operator", Freiburger IntervallBerichte 81/4, Freiburg, Germany, pp. 2537, 1981.
 L. Qi, "Bisubmodular functions", CORE Discussion paper 8901, Center for Operations Research & Econometrics, LouvainlaNeuve, Belgium, 1989.
 L. Qi, "On the set covering polytope and the MFMC clutter", AM89/19, Applied Mathematics Preprint, University of New South Wales, 1989.
 J.R. Birge X. Chen, L. Qi and Z. Wei, "A stochastic Newton method for solving stochastic quadratic programs with recourse", AMR 94/9, Applied Mathematics Report, University of New South Wales, 1994.
 L. Qi, "Cdifferential operators, Cdifferentiability and generalized Newton methods", AMR 96/5, Applied Mathematics Report, University of New South Wales, 1996.
 L. Qi, Analytical properties of the Huber and the median Mestimator interpolation problems?? 2003.
 S. Hu and L. Qi, "Convergence
of a second order Markov chain", July 2011,
Revised in December 2011. (submitted)
 K.C. Chang, L. Qi
and T. Zhang, "A survey on the spectral
theory of nonnegative tensors", April 2012.
(submitted)















