Welcome to Liqun's Homepage

 Professor Liqun Qi

 Department of Applied Mathematics
 The Hong Kong Polytechnic University
 Hong Hom,

 Office: HJ643

 Tel: +852-27664591
 e-mail: maqilq@polyu.edu.hk
 

· Education

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

  • Research Interests:

Analysis

Tensor Analysis for Multivariate Calculus

Optimization and Applications

Generalized Newton Methods
Mutivariate Polynomial Optimization with Applications in Signal Processing
Supply Chain Network Models and Manufacturing Network Flows
Variational Inequalities
Power Engineering Optimization

Computational Mathematics and Applications

Shape-Preserving Approximation with Applications in Option Price
Systems of Nonlinear Equations

  •  Research Grants

Chief Investigator: Tsinghua University Science Fund, 1985-1987
Chief Investigator: China Science Fund, 1986-1987
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), 1990-1991
Chief Investigator: ARC Grant, “Stochastic Programming”, (Qi), 1990-1992
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), 1992-1995
Chief Investigator: ARC Grant, “Stochastic Programs and Their Applications”, (Qi, Womersley and Tin-Loi), 1995-1997
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), 1997-1999
Chief Investigator: ARC Grant, “Smoothing and Accelerating Methods for Nonmonotone and Nondifferentiable Problems”, (Qi, Chen and Fukushima), 1998
Chief Investigator: ARC Grant, “SQP and QP-free Algorithms for Nonlinear Programming”, (Qi and Womersley), 1998-2000
Chief Investigator: ARC Grant, “Smoothing and Non-Interior Point Methods”, (Qi, Fukushima and Chen), 1999-2001
Chief Investigator: ARC Grant, “Newton-type 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”, 2000-2002
Principal Investigator: RGC (The Research Grant Council of Hong Kong) Grant, “Reformulation Methods in Optimization”, 2000-2003
Chief Investigator: ARC (Australian Research Council) Grant, “Generalized Newton Methods for Constrained Approximation Problems and Sum of Norms”, 2001-2003
Projector Leader: The Hong Kong Polytechnic University Postdoctoral Fellowship Scheme, “Newton-like Methods and Trust Region Methods”, 2001-2003
Chief Investigator: ARC (Australian Research Council) Discovery Grant, “Robust Reformulation Methods”, 2002-2004
Principal Investigator: RGC (The Research Grant Council of Hong Kong) Grant, “Robust Algorithms for Constrained Nonlinear Programs”, 2001-2004
Principal Investigator: RGC (The Research Grant Council of Hong Kong) Grant, “Semismooth Newton Methods for Constrained Approximation Problems”, 2002-2005
Projector Leader: The Hong Kong Polytechnic University Postdoctoral Fellowship Scheme, “Nonlinear Optimization: Theory, Algorithms and Applications”, 2003-2005
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”, 2003-2004
Principal Investigator: RGC (The Research Grant Council of Hong Kong) Grant, “Aggregate Reformulation Methods with Applications”, 2003-2006

Principal Investigator: RGC (The Research Grant Council of Hong Kong) Grant, “Multivariate Polynomial Optimization and Systems”, 2004-2007.

Chief Investigator: ARC Discovery Grant, “Constrained and Stable Solutions of Nonlinear and Semismooth Equations”, 2005-2007.

Projector Leader: The Hong Kong Polytechnic University Postdoctoral Fellowship Scheme, “Polynomial Optimization: Theory, Algorithms and Applications”, 2005-2007.

Principal Investigator: RGC (The Research Grant Council of Hong Kong) Grant, “Constrained and Unconstrained Nonsmooth Equation Methods”, 2005-2008.

  • Memberships

The Mathematical Programming Society (1986-1987, 1993-)
Australian Mathematical Society (1989-1992)
Hong Kong Mathematical Society (2001-)

  • Editorial Positions

Editorial member, Journal of Applied Mathematics and Computational Mathematics (Shanghai) (1985-1988)
Editorial member, Journal of Tsinghua University (Natural Sciences) (1985-1987)
Editorial member, Journal of Combinatorial Optimization (1995-)
Editorial member, Computational Optimization and Applications (2003-)
Editorial member, ESAIM: Control, Optimization and Calculus of Variations (2003-2005)

Editor, Pacific Journal of Optimization (2003-)

Editorial member, Journal of Industrial Management and Optimization (2003-)
Guest editor for Mathematical Programming Series B: Computational Nonsmooth Optimization (1997)
Guest editor for Journal of Computational and Applied Mathematics (2001)(2002)
Guest editor for Computational Optimization and Application (2000)(2003)
Guest editor for Annals of Operations Research (2001)
Guest editor for Journal of Global Optimization (2003)(2005)

  • Prizes and Honors

Championship of Mathematics Competition, Tsinghua University, 1963
Vilas Fellowship, 1982
Knapp Meeting Travel Fellowship, 1984
Andrew Mellon Postdoctoral Fellowship, 1984-1985
CORE Research Fellowship, 1988-1989
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, 1998-2000

Adjunct Professor of Mathematics, Tsinghua University, 2001-2004

Research Professor of Mathematics, Curtin University of

Technology, 2001-2004

Visiting Professor of Mathematics, Zhongshan University, 2001-2005

Adjunct Professor of Mathematics, Guangxi University, 2002-2006

Adjunct Professor of Mathematics and Computer Sciences, Nanjing Normal University, 2003-2006

Visiting Professor of Mathematics, University of New South Wales, 2003-2006

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

Plenary Speaker of Second International Symposium, ISORA’96, 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, Yichang-Chongqing, China, June, 2002
Plenary Speaker of The Second Japanese-Sino Optimization Meeting, Kyoto, Japan, September, 2002
Plenary Speaker of The Multi-Conference 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 China-Australia 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 Australia-China Workshop on Optimization, Ballarat, Australia, December, 2004

Foreign Member of the Petrovskaya Academy of Science and Art, Russia, (2003-)

ISI Most Highly Cited Scientist in 1981-1999: www.isihighlycited.com

The President’s Awards for Excellent Performance/Achievement 2003/2004, based upon Research and Scholarly Activities, The Hong Kong Polytechnic University.

  •  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.
Co-Chair of the Organizing Committee for the First Sino-Japan Optimization Meeting, Hong Kong, 2000.
Member of the Steering Committee for the Sino-Japan Optimization Meeting (2000-).
Director of the International Workshop on Optimization and Control with Applications, Erice, Italy, 2001.
General Co-Chair 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, hongqing-Chengdu-Jiuzhaigou, China, 2004.

  • Publications

A. Books and Edited Volumns.

 

1.         Q. Li, Z. Mo and L. Qi, Numerical Solutions of Nonlinear Systems, Science Press, Shanghai, 1987, Second Print: 1992, Third Print: 1997. (286 pages).

2.         D.Z. Du, L. Qi and R.S. Womersley (editors), Recent Advances in nonsmooth Optimization, World Scientific, New Jersey, 1995. (472 pages).

3.         L. Qi, A. Ruszczy\'nski and R.S. Womersley (editors), Computational Nonsmooth Optimization, Mathematical Programming Series B. 76, (North-Holland, Amsterdam, 1997) (163 pages).

4.         M. Fukushima and L. Qi (editors), Reformulation - Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, Kluwer Academic Publisher, Nowell, MA. USA, 1999. (442 pages).

5.         M. Fukushima and L. Qi (editors), Nonsmooth and Smoothing Methods, Computational Optimization and Applications, Special Issue, Kluwer Academic Publisher, Nowell, MA. USA, 2000. (189 pages).

6.         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).

7.         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).

8.         L. Qi, X. Yang and J. Zhang (editors), The First Sino-Japan Optimization Meeting, Journal of Computational and Applied Mathematics 146, Elsevier Science Publisher, Amsterdam, The Netherlands, 2002. (177 pages).

9.         L. Qi (editor), A Tribute to Eljah (Lucien) Polak, Computational Optimization and Applications 25, Kluwer Academic Publisher, Nowell, MA. USA, 2003. (311 pages).

10.     L. Qi, K.L. Teo and X. Yang (editors), Optimization and Control, Journal of Global Optimization, Special Issue, Kluwer Academic Publisher, Nowell, MA. USA, 2004. (100 pages).

11.     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, (Americal Institute of Mathematical Sciences, Springfield, MO, USA, 2005). (148 pages).

12.     L. Qi, K.L. Teo and X. Yang (editors), Optimization and Control with Applications, (Springer, New York, USA, 2005). (600 pages).

13.     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).

14.     M. Fukushima and L. Qi (editors), Optimization and Control with Applications, Computational Optimization and Applications, Special Issue, (Springer, New York, USA, 2005).

B. Papers in Refereed Journals

1.             Z.T. Chi and L. Qi, “Convex functionals of l-order”, Numerical Mathematics, A Journal of Chinese Universities, 1 (1979) 112-119.

2.             Z.T. Chi and L. Qi, “Some global inverse function theorems”, Numerical Mathematics, A Journal of Chinese Universities, 1 (1979) 215-216.

3.             L. Qi, “An improved Krawczyk-Moore interval iteration method”, Numerical Mathematics, A Journal of Chinese Universities, 2 (1980) 26-34.

4.             L. Qi, “Solving systems of nonlinear algebraic equations with exclusion Newton methods”, Numer. Comp. & Comp. Applic. 1 (1980) 109-115.

5.             L. Qi, “Interval boxes of solutions of nonlinear systems”, Computing, 27 (1981) 137-144.

6.             L. Qi, “A note on the Moore test for nonlinear system”, SIAM J. Numer. Anal. 19 (1982) 851-857.

7.             R.E. Moore and L. Qi, “A successive interval test for nonlinear systems”, SIAM J. Numer. Anal. 19 (1982) 845-850.

8.             L. Qi, “Interval analysis”, Oper. Res. (Shanghai) 1 (1982) 29-35.

9.             L. Qi, “Uniqueness of the maximal extension of a monotone operator”, Nonlinear Analysis, 7 (1983) 325-332.

10.         L. Qi, “Complete closedness of maximal monotone operators”, Mathematics of Operations Research,8 (1983) 315-317.

11.         L. Qi, “Some simple estimates for singular values of a matrix”, Linear Algebra & Its Applications, 56 (1984) 105-119.

12.         L. Qi, “Forest iteration method for stochastic transportation problem”, Mathematical Programming Study, 25 (1985) 142-163.

13.         L. Qi, “Three pearls in mathematical programming”, Nature Journal (Shanghai), 8 (1985) 299- 306.

14.         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.

15.         L. Qi, “An alternating method for stochastic linear programming with simple recourse”, Mathematical Programming Study, 27 (1986) 182-190.

16.         L. Qi, “The A-forest iteration method for the stochastic generalized transportation problem”, Mathematics of Operations Research, 12 (1987) 1-21.

17.         L. Qi, “Total unimodularity via directed subsets”, Advances in Mathematics, 16 (1987) 332.

18.         L. Qi, “Odd submodularity and discrete convexity”, Advances in Mathematics, 16 (1987) 427-429.

19.         L. Qi, “Odd submodular functions, Dilworth functions and discrete convex functions”, Mathematics of Operations Research, 3 (1988) 435-446.

20.         L. Qi, “Directed submodularity, ditroids and directed submodular flows”, Mathematical Programming, 42 (1988) 579-599.

21.         J.R. Birge and L. Qi, “Computing block-angular Karmarkar projections with applications to stochastic programming”, Management Science , 34 (1988) 1472-1479.

22.         L. Qi and X. Tu, “The dual forest iteration method for the stochastic transportation problem”, Journal of Tsinghua Univ. , 28 (1988) 74-82.

23.         L. Qi, “The maximal normal operator space and integration of subdifferentials of nonconvex functions”, Nonlinear Analysis, 13 (1989) 1003-1011.

24.         L. Qi, “Semismoothness and decomposition of maximal normal operators”, Journal of Mathematical Analysis & Applications, 146 (1990) 271-279.

25.         L. Qi, “Quasidifferentials and maximal normal operators”, Mathematical Programming,49 (1991) 263-271.

26.         J.V. Burke and L. Qi, “Weak directional closedness and generalized subdifferentials”, Journal of Mathematical Analysis & Applications, 159 (1991) 485-499.

27.         G. Gwan and L. Qi, “On facets of the three-index assignment polytope”, Australasian Journal of Combinatorics , 6 (1992) 67-87.

28.         J. Sun and L. Qi, “An interior point algorithm of  iterations for C1-convex programming”, Mathematical Programming, 57 (1992) 239-257.

29.         L. Qi, “Convergence analysis of some algorithms for solving nonsmooth equations”, Mathematics of Operations Research, 18 (1993) 227-244.

30.         L. Qi and J. Sun, “A nonsmooth version of Newton's method”, Mathematical Programming, 58 (1993) 353-368.

31.         E. Balas and L. Qi, “Linear-time separation algorithms for the three-index assignment polytope”, Discrete Applied Mathematics, 43 (1993) 1-12.

32.         J.S. Pang and L. Qi, “Nonsmooth equations: motivation and algorithms”, SIAM Journal on Optimization, 3 (1993) 443-465.

33.         J.R. Birge and L. Qi, “Semiregularity and generalized subdifferentials with applications to optimization”, Mathematics of Operations Research, 18 (1993) 982-1005.

34.         X. Chen and L. Qi, “A parameterized Newton method and a quasi-Newton method for solving nonsmooth equations”, Computational Optimization and Applications, 3 (1994) 157-179.

35.         L. Qi, “Superlinearly convergent approximate Newton methods for LC1 optimization problems”, Mathematical Programming, 64 (1994) 277-294.

36.         L. Qi and H. Jiang, “On the range sets of variational inequalities”, Journal of Optimization Theory and Applications, 83 (1994) 565-585.

37.         L. Qi and J. Sun, “A trust region algorithm for minimization of locally Lipschitzian functions”, Mathematical Programming , 66 (1994) 25-43.

38.         L. Qi, “Trust region algorithms for solving nonsmooth equations”, SIAM Journal on Optimization, 5 (1995) 219-230.

39.         L. Qi and X. Chen, “A globally convergent successive approximation method for severely nonsmooth equations”, SIAM Journal on Control and Optimization, 33 (1995) 402-418.

40.         J.R. Birge and L. Qi, “Subdifferentials in approximation for stochastic programming”, SIAM Journal on Optimization, 5 (1995) 436-453.

41.         J.S. Pang and L. Qi, “A globally convergent Newton method for convex SC1 minimization problems”, Journal of Optimization Theory and Applications, 85 (1995) 633-648.

42.         R. Poliquin and L. Qi, “Iteration functions in some nonsmooth optimization algorithms”, Mathematics of Operations Research, 20 (1995) 479-496.

43.         J.R. Birge and L. Qi, “Continuous approximation schemes for solving stochastic programs”, Annals of Operations Research, 56 (1995) 15-38.

44.         L. Qi and R. Womersley, “An SQP Algorithm for extended linear-quadratic problems in stochastic programming”, Annals of Operations Research, 56 (1995) 251-285.

45.         X. Chen, L. Qi, and R. Womersley, “Newton's method for quadratic stochastic programs with recourse”, Journal of Computational and Applied Mathematics, 60 (1995) 29-46.

46.         J.M. Martinez and L. Qi, “Inexact Newton methods for solving nonsmooth equations”, Journal of Computational and Applied Mathematics, 60 (1995) 127-145.

47.         H. Jiang and L. Qi, “Local Uniqueness and convergence of iterative methods for nonsmooth variational inequalities”, Journal of Mathematical Analysis & Applications, 196 (1995) 314-331.

48.         L. Qi and W. Sun, “A class of iterative methods for minimax problems”, Numerical Mathematics, A Journal of Chinese Universities, Series B, 4 (1995) 237-239.

49.         J.L. Nazareth and L. Qi, “Globalization of Newton's method for solving nonlinear equations”, Journal of Numerical Algebra with Applications, 3, (1996) 239-249.

50.         H. Jiang and L. Qi, “Globally and superlinearly convergent trust region algorithm for convex SC1 minimization problems and its application to stochastic programs”, Journal of Optimization Theory and Applications, 90 (1996) 649-670.

51.         Z. Wei and L. Qi, “Convergence analysis of a proximal Newton method”, Numerical Functional Analysis and Optimization, 17 (1996) 463-472.

52.         M. Fukushima and L. Qi, “A globally and superlinearly convergent algorithm for nonsmooth convex minimization”, SIAM Journal on Optimization, 6 (1996) 1106-1120.

53.         L. Qi and R.S. Womersley, “On extreme singular values of matrix valued functions”, Journal of Convex Analysis, 3 (1996) 153-166.

54.         F. Tin-Loi, L. Qi, Z. Wei and R.S. Womersley, “Stochastic ultimate load analysis: Models and solution method”, Numerical Functional Analysis and Optimization, 17 (1996) 1029-1043.

55.         H. Jiang and L. Qi, “A new nonsmooth equations approach to nonlinear complementarity problems”, SIAM Journal on Control and Optimization, 35 (1997) 178-193.

56.         L. Qi and X. Chen, “A preconditioning proximal Newton method for nondifferentiable convex optimization”, Mathematical Programming, 76 (1997) 411-429.

57.         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) 445-462.

58.         L. Qi and H. Jiang, “Semismooth Karush-Kuhn-Tucker equations and convergence analysis of Newton methods and quasi-Newton methods for solving these equations”, Mathematics of Operations Research, 22 (1997) 301-325.

59.         L. Qi, “On superlinear convergence of quasi-Newton methods for nonsmooth equations”, Operations Research Letters , 20 (1997) 223-228.

60.         Z. Wei, L. Qi and H. Jiang, “Some convergence properties of descent methods”, Journal of Optimization Theory and Applications, 95 (1997) 177-188.

61.         H. Jiang, M. Fukushima, L. Qi and D. Sun, “A trust region method for solving generalized complementarity problems”, SIAM Journal on Optimization, 8 (1998) 140-157.

62.         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) 357-383.

63.         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) 519-540.

64.         R. Mifflin, D. Sun and L. Qi, “Quasi-Newton bundle-type methods for nondifferentiable convex optimization”, SIAM Journal on Optimization, 8 (1998) 583-603.

65.         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) 1005-1019.

66.         Z. Wei, L. Qi and J. Birge, “A new method for nonsmooth convex optimization”, Journal of Inequalities and Applications, 2 (1998) 157-179.

67.         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) 141-158.

68.         F. Potra, L. Qi and D. Sun, “Secant methods for semismooth equations”, Numerische Mathematik, 80 (1998) 305-324.

69.         R. Mifflin, L. Qi and D. Sun, “Properties of the Moreau-Yosida regularization of a piecewise C2 convex function”, Mathematical Programming, 84 (1999) 269-281.

70.         F. Facchinei, H. Jiang and L. Qi, “A smoothing method for mathematical programs with equilibrium constraints”, Mathematical Programming, 85 (1999) 107-134.

71.         L. Qi, “Regular pseudo-smooth NCP and BVIP functions and globally and quadratically convergent generalized Newton methods for complementarity and variational inequality problems”, Mathematics of Operations Research, 24 (1999) 440-471.

72.         E. Polak, L. Qi and D. Sun, “First-order algorithms for generalized finite and semi-finite min-max problems”, Computational Optimization and Applications, 13 (1999) 137-161.

73.         D. Sun and L. Qi, “On NCP functions”, Computational Optimization and Applications, 13 (1999) 201-220.

74.         L. Qi and D. Sun, “Improving the convergence of non-interior point algorithms for nonlinear complementarity problems”, Mathematics of Computation, 69 (2000) 283-304.

75.         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) 1-35.

76.         J.R. Birge, L. Qi and Z. Wei, “A variant of the Topkins-Veinott method for solving inequality constrained optimization problems”, Journal of Applied Mathematics and Optimization, 41 (2000) 309-330.

77.         L. Qi and Z. Wei, “On the constant positive linear independence condition and its application to SQP methods”, SIAM Journal on Optimization, 11 (2000) 963-981.

78.         H. Qi and L. Qi, “A new QP-free, globally convergent, locally superlinearly convergent algorithm for inequality constrained optimization”, SIAM Journal on Optimization,11 (2000) 113-132.

79.         X. Chen, Z. Nashed and L. Qi, “Smoothing methods and semismooth methods for nondifferentiable operator equations”, SIAM Journal on Numerical Analysis, 38 (2000) 1200-1216.

80.         L. Qi and G. Zhou, “ A smoothing Newton method for minimizing a sum of Euclidean norms”, SIAM Journal on Optimization, 11 (2000) 389-410.

81.         L. Qi, “On an extended Lagrange claim”, Journal of Optimization Theory and Applications,108 (2001) 687-690.

82.         A.L. Dontchev, H. Qi and L. Qi, “Convergence of Newton's method for convex best interpolation”, Numerische Mathematik, 87 (2001) 435-456.

83.         D. Sun and L. Qi, “Solving variational inequality problems via smoothing-nonsmooth reformulations”, Journal of Computational and Applied Mathematics, 129 (2001) 37-62.

84.         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) 343-359.

85.         Q. Han, L.Z. Liao, H. Qi and L. Qi, “Stability analysis of gradient-based neural networks for optimization problems”, Journal of Global Optimization,19 (2001) 363-381.

86.         E. Polak, L. Qi and D. Sun, “Second-order algorithms for generalized finite and semi-infinite min-max problems”, SIAM Journal on Optimization, 11 (2001) 937-961.

87.         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) 1145-1146.

88.         L. Qi and G. Zhou, “A smoothing Newton method for ball constrained variational inequalities with applications”, Computing [Suppl], 15 (2001) 211-225.

89.         L. Qi and Y. Yang, “A globally and superlinearly convergent SQP algorithm for nonlinear constrained optimization”, Journal of Global Optimization, 21 (2001) 157-184.

90.         L. Qi, D. Sun and G. Zhou, “A primal-dual algorithm for minimizing a sum of Euclidean norms”, Journal of Computational and Applied Mathematics, 138 (2002) 127-150.

91.         X. Chen, L. Qi and Y. Yang, “Lagrangian globalization methods for nonlinear complementarity problems”, Journal of Optimization Theory and Applications, 112 (2002) 77-95.

92.         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) 121-147.

93.         L. Qi and Y. Yang, “A globally and superlinearly convergent QP-free algorithm for nonlinear constrained optimization”, Journal of Optimization Theory and Applications,113 (2002) 297-323.

94.         X. Tong, D. Li and L. Qi, “An iterative method for solving semismooth equations”, Journal of Computational and Applied Mathematics, 146 (2002) 1-10.

95.         L. Qi and Y. Yang, “NCP functions applied to Lagrangian globalization for the nonlinear complementarity problem”, Journal of Global Optimization, 24 (2002) 261-283.

96.         A.L. Dontchev, H. Qi, L. Qi and H. Yin, “A Newton method for shape-preserving spline interpolation”, SIAM Journal on Optimization, 13 (2003) 588-602.

97.         G. Gu, D. Li, L. Qi and S. Zhou, “Descent directions of quasi-Newton methods for symmetric nonlinear equations”, SIAM Journal on Numerical Analysis, 40 (2003) 1763-1774.

98.         A.L. Dontchev, H. Qi and L. Qi, “Quadratic convergence of Newton's method for convex interpolation and smoothing”, Constructive Approximation, 19 (2003) 123-143.

99.         Z. Wei, L. Qi and X. Chen, “An SQP-type method and its application in stochastic programming”, Journal of Optimization Theory and Applications, 116 (2003) 205-228.

100.     C. Kanzow, H. Qi and L. Qi, “On the minimum norm solution of linear programs”, Journal of Optimization Theory and Applications, 116 (2003) 333-345.

101.     L. Qi and H. Yin, “A strongly semismooth integral function and its application”, Computational Optimization and Applications, 25 (2003) 223-246.

102.     Y. Yang, D. Li and L. Qi, “A feasible sequential linear equation method for inequality constrained optimization”,
SIAM Journal on Optimization,13 (2003) 1222-1244.

103.     S.C. Fang and L. Qi, “Manufacturing network flows: A generalized network model for manufacturing process modelling”, Optimization Methods and Software, 18 (2003) 143-165.

104.     L. Qi and K.L. Teo, “Multivariate polynomial minimization and its application in signal processing”, Journal of Global Optimization, 46 (2003) 419-433.

105.     L. Qi, S.Y. Wu and G. Zhou, “Semismooth Newton methods for solving semi-infinite programming problems”, Journal of Global Optimization, 47 (2003) 215-232.

106.     H. Qi and L. Qi, “Finite termination of a dual Newton method for convex best C1 interpolation and smoothing”, Numerische Mathematik 96 (2003) 317-337.

107.     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) 439-463.

108.     L. Qi, X. Tong and D. Li, “An active-set projected trust region algorithm for box constrained nonsmooth equations”, Journal of Optimization Theory and Applications 120 (2004) 601-625.

109.     Y. Wang, H. Yin and L. Qi, “No-Arbitrage interpolation of the option price function and its reformulation”, Journal of Optimization Theory and Applications 120 (2004) 627-649.

110.     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) 99-109.

111.     L.Z. Liao, H. Qi and L. Qi, “Neurodynamical optimization”, Journal of Global Optimization 28 (2004) 175-195.

112.     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) 783-806.

113.     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) 131-147.

114.     Z. Huang, L. Qi and D. Sun, “Sub-quadratic convergence of a smoothing Newton algorithm for the P0– and monotone LCP”, Mathematical Programming 99 (2004) 423-441.

115.     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) 187-212.

116.     D. Li, L. Qi, J. Tam and S.Y. Wu, “A smoothing Newton method for semi-infinite programming”, Journal of Global Optimization 30 (2004) 169-194.

117.     X. Chen, H. Qi, L. Qi and K.L. Teo, “Smooth convex approximation to the maximum eigenvalue function”, Journal of Global Optimization 30 (2004) 253-270.

118.     L. Qi, “Extrema of a real polynomial”, Journal of Global Optimization 30 (2004) 405-433.

119.     Y. Yang and L. Qi, “Smoothing trust region methods for nonlinear complementarity problems with P0 functions”, Annals of Operations Research 133 (2005) 99-117.

120.     C. Ling, X. Chen, M. Fukushima and L. Qi, “A smoothing implicit programming approach for solving a class of stochastic generalized semi-infinite programming problems”, Pacific Journal of Optimization 1 (2005) 127-145.

121.     J. Mo, L. Qi and Z. Wei, “A network simplex algorithm for simple manufacturing network model”, Journal of Industrial Management and Optimization 1 (2005) 251-273.

122.     L. Qi, Z. Wan and Y. Yang, “Global minimization of normal quartic polynomials based on global descent directions”, SIAM Journal on Optimization 15 (2005) 275-302.

123.     L. Qi, A. Shapiro and C. Ling, “Differentiability and semismoothness properties of integral functions and their applications”, Mathematical Programming 102 (2005) 223-248.

124.     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.

125.     L.Z. Liao, L. Qi and H.W. Tam, “A gradient-based continuous method for large-scale optimization problems”,  Journal of Global Optimization 31 (2005) 271-286.

126.     X. Tong, L. Qi and Y. Yang, “The Lagrangian globalization method for nonsmooth constrained equations”, to appear in: Computational Optimization and Applications.

127.     S.Y. Wu, D. Li, L. Qi and G. Zhou, “An iterative method for solving KKT system of the semi-infinite programming”, to appear in: Optimization Methods and Software.

128.     X. Zhang, Y. Wang and L. Qi, “Unconstrained optimization reformulation of the generalized complementarity problem and its applications”, to appear in: Optimization.

129.     L. Qi, “Eigenvalues of an even-order real supersymmetric tensor”, to appear in: Journal of Symbolic Computation.

130.     J. Mo, L. Qi and Z. Wei, “A manufacturing supply chain optimization model for distilling process”, to appear in: Applied Mathematics and Computation.

131.     C. Ling, L. Qi, G. Zhou and S.Y. Wu, “Global convergence of a robust smoothing SQP method for semi-infinite programming”, to appear in: Journal of Optimization Theory and Applications.

132.     H. Qi, L. Qi and X. Yang, “Deriving sufficient conditions for global asymptotic stability of delayed cellular neural networks via nonsmooth analysis II", to appear in: IEEE Transactions on Neural Networks.

133.     X.B. Gao, L.Z. Liao and L. Qi, “A novel neural network for variational inequalities with linear and nonlinear constraints”, to appear in: IEEE Transactions on Neural Networks.

134.     L. Qi, “Boundedness and regularity properties of semismooth reformulations of variational inequalities”, to appear in: Journal of Global Optimization.

C. Papers in Edited Books

1.            L. Qi, “A generalization of the Krawczyk-Moore Algorithm”, in: Interval Mathematics 1980, K. Nickel ed. (Academic Press, New York, 1981) 481-488.

2.            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) 283-300.

3.            L. Qi, E. Balas and G. Gwan, “A new facet class and a polyhedral method for the three-index assignment problem”, in: New Advances in Optimization and Approximation, D.Z. Du and J. Sun eds., (Kluwer Academic Publisher, Nowell, MA. USA, 1994) 256-274.

4.            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) 55-67.

5.            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) 197-212.

6.            L. Qi, “LC1 functions and LC1 optimization”, invited paper, Operations Research and Its Application, D.Z. Du, X.S. Zhang and K. Cheng eds., (World Publishing, Beijing, 1996) 4-13.

7.            D. Sun, M. Fukushima and L. Qi, “A computable generalized Hessian of the D-gap function and Newton-type 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) 452-473.

8.            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) 421-442.

9.            L. Qi, “Second-Order Analysis of the Moreau-Yoshida Regularization”, Nonlinear Analysis and Convex Analysis, W. Takahashi and T. Tanaka, eds., (World Scientific Publishing Co., London, 1999) 16-25.

10.        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) 121-146.

11.        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) 317-350.

12.        J.R. Birge, S.M. Pollock and L. Qi, “A quadratic recourse function for the two-stage 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) 109-121.

13.        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) 91-107.

14.        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) 100-104.

15.        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) 261-270.

16.        L. Qi, “Shape-preserving 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) 67-80.

17.        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) 103-114.

18.        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) 405-413.

19.        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), 42-55.

20.        L. Qi, “Semismooth Newton methods for shape-preserving interpolation, option price and semi-infinite programs”, Variational Analysis and Applications, F. Giannessi and A. Maugeri, eds., (Kluwer Academic Publisher, Nowell, MA. USA, 2005) 905-919.