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Qi HouDuo (戚厚铎)
Department of Applied Mathematics
The Hong Kong Polytechnic University
Hung Hom, Kowloon, Hong Kong
Contact information
 Phone: +852 2766 4401
 Office: TU708, Yip Kit Chuen Building
 Email: houduo.qi@polyu.edu.hk
Education and Academic Qualifications
 PhD in Operational Research (1996), Institute of Applied Mathematics, Chinese Academy of Sciences
 MSc in Operational Research (1993), Qufu Normal University
 BSc in Statistics (1990), Peking University
Research Interests
 Numerical Optimization
 Data Science
 Portfolio Optimization
Publications (Google Scholar)
 Preprints
 Yitian Qian, Shaohua Pan, Shujun Bi, Houduo Qi, Error bounds for rankone DNN reformulation of QAP and DC exact penalty approach. arXiv:2403.11210, 2024.
 Penghe Zhang, Naihua Xiu, HouDuo Qi. Sparse SVM with HardMargin Loss: a NewtonAugmented Lagrangian Method in Reduced Dimensions. arXiv:2307.16281, 2023.
 Penghe Zhang, Naihua Xiu, HouDuo Qi. iNALM: An inexact Newton Augmented Lagrangian Method for ZeroOne Composite Optimization. arXiv:2306.08991, 2023.
 Chao Ding, HouDuo Qi. An Optimization Study of Diversification Return Portfolios. arXiv:2303.01657, 2023.
 Publications
 Deliang Yang and Houduo Qi. Supervised Maximum Variance Unfolding. To appear in: Machine Learning, 2024.
 Shaoyan Guo, HouDuo Qi, Liwei Zhang, Perturbation analysis of the Euclidean distance matrix optimization problem and its numerical implications. Computational Optimization and Applications, 2023.
 HouDuo Qi, Geometric characterization of maximum diversification return portfolio via Rao's quadratic entropy. SIAM Journal on Financial Mathematics 14(2), 525556, 2023.
 Chen Zhao, Naihua Xiu, Houduo Qi, and Ziyan Luo, A Lagrange–Newton algorithm for sparse nonlinear programming. Mathematical Programming 95, 903923, 2022.
 Jian Shen, JeinShan Chen, Houduo Qi, and Naihua Xiu, A penalized method of alternating projections for weighted lowrank Hankel matrix optimization. Mathematical Programming Computation 14, 417–450, 2022.
 Shenglong Zhou, Naihua Xiu, and Houduo Qi, Global and quadratic convergence of Newton hardthresholding pursuit, Journal Machine Learning Research 22(12), 599643, 2021.
 Shenglong Zhou, Lili Pan, Naihua Xiu, and Houduo Qi, Quadratic convergence of smoothing Newton's method for 0/1loss optimization. SIAM Journal Optimization 31, 31843211, 2021
 Hongxin Zhao, Lingchen Kong, and Houduo Qi, Optimal portfolio selections via $\ell_{12}$‑norm regularization. Computational Optimization and Applications 80, 853881, 2021.
 Houduo Qi, On the longonly minimum variance portfolio under single factor model. Operations Research Letters 49, 795801, 2021
 Shenglong Zhou, Naihua Xiu, and Houduo Qi, Robust Euclidean embedding via EDM optimization. Mathematical Programming Computation 12, 337387, 2020.
 Yue Lu, ChingYu Yang, JeinShan Chen, and Houduo Qi, The decompositions of nonsymmetric cones. Journal of Global Optimization 76, 155188, 2020.
 Lingchen Kong, Chuanqi Qi, and Houduo Qi, Classical multidimensional scaling: a subspace perspective, overdenoising and outlier detection. IEEE Transactions on Signal Processing 67, 38423857, 2019.
 Chen Zhao, Ziyan Luo, Weiyue Li, Houduo Qi, and Naihua Xiu, Lagrangian duality and saddle points for sparse linear programming Science China Mathematics 62, 20152032, 2019.
 Shenglong Zhou, Naihua Xiu, and Houduo Qi, A fast matrix majorizationprojection method for penalized stress minimization with box constraints. IEEE Transactions on Signal Processing 66, 43314346, 2018.
 Houduo Qi, Jian Shen, and Naihua Xiu, A sequential majorization method for approximating weighted time series of finite rank. Statistics and Its Interface 11, 615630, 2018.
 Xianchao Xiu, Lingchen Kong, Yan Li, and Houduo Qi, Iterative reweighted methods for L1 minimization. Computational Optimization and Applications 70, 201219, 2018.
 Lili Pan, Shenglong Zhou, Naihua Xiu, and Houduo Qi, A convergent iterative gard thresholding for nonnegative sparsity optimization. Pacific Journal of Optimization 13, 325353, 2017.
 Chao Ding and Houduo Qi, Convex optimization learning of faithful Euclidean distance representations in nonlinear dimensionality reduction. Mathematical Programming 164 341381, 2017.
 Qingna Li and Houduo Qi, An inexact smoothing Newton method for Euclidean distance matrix optimization under ordinal constraints. Journal of Computational Mathematics 35, 467483, 2017.
 Chao Ding and Houduo Qi, Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation. Computational Optimization and Applications 66, 187218, 2017.
 Houduo Qi, A convex matrix optimization for the additive constant problem in multidimensional scaling with application to locally linear embedding. SIAM Journal on Optimization 26, 25642590, 2016.
 Shuanghua Bai and Houduo Qi, Tackling the flip ambiguity in wireless sensor network localization and beyond. Digital Signal Processing 26, 8597, 2016.
 Shenglong Zhou, Naihua Xiu, Yingnan Wang, Lingchen Kong, and Houduo Qi, A nullspacebased weighted l1minimization approach to compressed sensing. Information and Inference 5, 76102, 2016.
 Sohan Jahan and Houduo Qi, Regularized multidimensional scaling with radial basis functions. Journal of Industrial Management and Optimization 12, 543563, 2016.
 Shuanghua Bai, Houduo Qi, and Naihua Xiu, Constrained best Euclidean distance embedding on a sphere: a Matrix optimization approach. SIAM J. Optimization 25, 439467, 2015.
 Chao Ding and Houduo Qi, A computable characterization of the extrinsic mean of reflection shapes and its asymptotic properties. Asia Pacific Journal of Operational Research 32, 1540005, 2015.
 Houduo Qi and Xiaoming Yuan, Computing the nearest Euclidean distance matrix with low embedding dimensions. Mathematical Programming, 147, 351389, 2014.
 Houduo Qi, Conditional quadratic semidefinite programming: Examples and methods. Journal of Operations Research Society of China 2, 143170, 2014.
 Houduo Qi, Naihua Xiu, and Xiaoming Yuan, A Lagrangian dual approach to the single source localization problem. IEEE Transactions on Signal Processing 61, 38153826, 2013.
 Houduo Qi, A semismooth Newton method for the nearest Euclidean distance matrix problem. SIAM Journal on Matrix Analysis and Applications 34, 6793, 2013.
 Houduo Qi and Naihua Xiu, A convex quadratic semidefinite programming approach to the partial additive constant problem in multidimensional scaling. Journal of Statistical Computation and Simulation 82, 13171336, 2012.
 Qingna Li and Houduo Qi, A sequential semismooth Newton method for the nearest lowrank correlation matrix problem. SIAM Journal on Optimization 21, 16411666, 2011.
 Houduo Qi, A semidefinite programming study of the Elfving theorem. Journal of Statistical Planning and Inference 141, 31173130, 2011.
 Qingna Li, Houduo Qi, and Naihua Xiu, Block relaxation and majorization methods for the nearest correlation matrix with factor structure. Computational Optimization and Applications 50, 327349, 2011.
 Houduo Qi and Defeng Sun, An augmented Lagrangian dual approach for the $H$weighted nearest correlation matrix problem. IMA Journal on Numerical Analysis 31, 491511, 2011.
 Houduo Qi and Defeng Sun, Correlation stress testing for valueatrisk: an unconstrained convex optimization approach. Computational Optimization and Applications 25, 427462, 2010.
 Qingna Li, Donghui Li, and Houduo Qi, Newton's method for computing the nearest correlation matrix with a simple upper bound. Journal of Optimization Theory and Applications 147, 546568, 2010.
 Houduo Qi, Local duality of nonlinear semidefinite programming. Mathematics of Operations Research 34, 124141, 2009.
 Houduo Qi, Positive semidefinite matrix completions on chordal graphs and constraint nondegeneracy in semidefinite programming. Linear Algebra and Its Applications 430, 11511164, 2009.
 Houduo Qi, New sufficient conditions for global robust stability of delayed neural networks. IEEE Transactions on Circuits and Systems I: Regular Papers 54, 11311141, 2007.
 Houduo Qi, Zhonghang Xia, and G.Xing, An application of the nearest correlation matrix to Web document classification. Journal of Industrial Management and Optimization 3, 701713, 2007.
 Houduo Qi and Xiaoqi Yang, Regularity and wellposedness of a dual program for convex best C1spline interpolation. Computational Optimization and Applications 37, 409425, 2007.
 Houduo Qi and Defeng Sun, A quadratically convergent Newton method for the nearest correlation matrix problem. SIAM J. Matrix Analysis and Applications 28, 360385, 2006.
 Xin Chen and Houduo Qi, Cartesian Pproperty and its applications to the semidefinite linear Complementarity problem. Mathematical Programming 106, 177201, 2006.
 Houduo Qi and Xiaoqi Yang, Armijo Newton method for convex best interpolation. Optimization Methods and Software 21, 179200, 2006.
 Houduo Qi and Xiaoqi Yang, Deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis II. IEEE Transactions on Neural Networks 16, 17011706, 2005.
 Houduo Qi and Liqun Qi, Deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis. IEEE Transactions on Neural Networks 14, 99109, 2004.
 Houduo Qi and Xiaoqi Yang, Semismoothness of spectral functions. SIAM Journal on Matrix Analysis and Applications 25, 784803, 2004.
 Xin Chen, Houduo Qi, Liqun Qi, and KokLay Teo, Smooth convex approximation to the maximum eigenvalue function. Journal of Global Optimization 30, 253270, 2004.
 Lizhi Liao, Houduo Qi, and Liqun Qi, Neurodynamic optimization. Journal of Global Optimization 28, 175195, 2004.
 Houduo Qi, Liqun Qi, and Defeng Sun, Solving KKT systems via the trust region and the conjugate gradient methods. SIAM Journal on Optimization 14, 439463, 2003.
 Houduo Qi and Liqun Qi, Finite termination of a dual Newton method for convex best C1 interpolation and smoothing. Numerische Mathematik 96, 317337, 2003.
 Xin Chen, Houduo Qi, and Paul Tseng, Analysis of nonsmooth symmetricmatrixvalued functions with applications to semidefinite complementarity problems. SIAM Journal on Optimization 13, 960985, 2003.
 Asen L. Dontchev, Houduo Qi, and Liqun Qi, Quadratic convergence of Newton's method for convex interpolation and smoothing. Constructive Approximation 19, 123143, 2003.
 Christian Kanzow, Houduo Qi, and Liqun Qi, On the minimum normal solution of linear programs. Journal of Optimization Theory and Applications 116, 333345, 2003.
 Defeng, Robert S Womersley, and Houduo Qi, A feasible semismooth asymptotically Newton method for mixed complementarity problems. Mathematical Programming 94, 167187, 2002.
 Asen L. Dontchev, Houduo Qi, Liqun Qi, and Hongxia Yin, A Newton method for shapepreserving spline interpolation. SIAM Journal on Optimization 13, 588602, 2002.
 Qiaoming Han, Lizhi Liao, Houduo Qi, and Lizhi Liao, Stability analysis of gradientbased neural networks for optimization problems. Journal of Global Optimization 19, 363381, 2001.
 Lizhi Liao, Houduo Qi, and Liqun Qi, Solving nonlinear complementarity problems with neural networks: a reformulation method approach. Journal of Computational and Applied Mathematics 131, 343359, 2001.
 Asen L. Dontchev, Houduo Qi, and Liqun Qi, Convergence of Newton's methods for convex best interpolation. Numerische Mathematik 87, 435456, 2001.
 Houduo Qi and Liqun Qi, A new QPfree, globally convergent and locally superlinearly convergent algorithm for the inequality constrained optimization. SIAM Journal on Optimization 11, 113132, 2000.
 Houduo Qi and lizhi Liao, A smoothing Newton method for general nonlinear complementarity problems. Computational Optimization and Applications 17, 231253, 2000.
 Houduo Qi, A regularized smoothing Newton method for box constrained variational inequality problems with $P_0$functions. SIAM Journal on Optimization 10, 315330, 2000.
 Houduo Qi and Yuzhong Zhang, A globally derivativefree descent method for nonlinear complementarity problems. Journal of Computational Mathematics 18, 251264, 2000.
 Christian Kanzow and Houduo Qi, A QPfree constrained Newtontype method for variational inequality problems. Mathematical Programming 85, 81106, 1999.
 Houduo Qi and Lizhi Liao, A smoothing Newtontype method for extended vertical linear complementarity problems. SIAM Journal on Matrix Analysis and Applications 21, 4566, 1999.
 Lizhi Liao and Houduo Qi, A neural network for the linear complementarity problem. Mathematical and Computer Modelling 29, 918, 1999.
 Houduo Qi, Lizhi Liao, and Zhenghua Lin, Regularized smoothing approximations to vertical nonlinear complementarity problems. Journal of Mathematical Analysis and Applications 230, 261276, 1999.
 Houduo Qi, On stationary and minimizing sequences of a new class of merit functions for nonlinear complementarity problems. Journal of Optimization Theory and Applications 102, 411431, 1999.
 Houduo Qi, Tikhonov regularization methods for general variational inequality problems. Journal of Optimization Theory and Applications 102, 93101, 1999.
 Yunbin Zhao, Jiye han, and Houduo Qi, Exceptional families and existence theorems for variational inequality problems. Journal of Optimization Theory and Applications 101, 475495, 1999.
 Houduo Qi, A monotone property of the projection operator onto closed convex sets. J. Math. Res. Exposition 18, 580582, 1998.
 Guanghui Liu, Jieye han, Houduo Qi and Zhongling Xu, Convergence analysis of a class of conjugate gradient methods without sufficient decrease condition. Acta Math. Sci. (English Ed.), 1998, 18, 1116.
 Houduo Qi and Jieye Han, Exceptional family and existence theorems in linear complementarity problems. Mathematica Numerica Sinica, 1997, 19, 7077.
 Houduo Qi, Jiye Han and Guanghui Liu, Modified HestenesStiefel conjugate gradient methods. Chinese Annual of Mathematics, 1996, 17, 277284.
Grants

Rank2 Optimization Model for Multidimensional Scaling Graph Drawing (Role: PI, 20202022)
The Royal Society. 
EDM Optimization: a new paradigm for dimension reduction (Role: PI, 20192021)
The Alan Turing Institute.  To be added ...
Codes

NHTP:
solves the sparsity constrained optimization including CS, LR, LCP and
etc.
Global and quadratic convergence of Newton hardthresholding pursuit.
Teaching
 Under construction: Optimization Methods (graduate)
Group
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