Submitted
- S.L. Zhou, L.L. Pan, N.H. Xiu and H.D. Qi, 2021
Quadratic convergence of Newton's method for 0/1 loss optimization
SIAM J. Optimization, to appear. RG, ArXiv - Hongxin Zhao, Lingchen Kong, and Houduo Qi, 2021
Optimal Portfolio Selections via $\ell_{1, 2}$-norm Regularization
Computational Optimization and Applications, to appear. Submitted version - Jian Shen, Jein-Shan Chen, Hou-Duo Qi, and Naihua Xiu, 08/2020 (revised 05/2021)
A Penalized Method of Alternating Projections for Weighted Low-Rank Hankel Matrix Optimization, Code - Chen Zhao, Naihua Xiu, Houduo Qi, and Ziyan Luo, 04/2020 (revised 02/2021)
A Lagrange-Newton Algorithm for Sparse Nonlinear Programming.
Published
On the Long-only Minimum Variance Portfolio Under Single Factor Model
Operations Research Letter, 49 (2021), 795–801. ORL,
Global and quadratic convergence of Newton hard-thresholding pursuit
Journal of Machine Learning Research, 22(12):1−45, 2021. JMLR, RG, ArXiv, Code
Robust euclidean embedding via EDM optimization
Mathematical Programming Computation, 12(3): 337–387, 2020. MPC, Code
The decompositions of non-symmetric cones
Journal of Global Optimization, 76 (2020), 155-188.
Classical multidimensional scaling: a subspace perspective, over-denoising and outlier detection,
Codes: fsmds.m and ssmds.m
IEEE Transactions on Signal Processing, 67 (2019), 3842--3857.
Lagrangian duality and saddle points for sparse linear programming
Science China Mathematics, 62 (2019), 2015-2032.
Euclidean distance matrix optimization for sensor network localization,
In: C. Gao, G. Zhao and H. Fourati, ed., Cooperative Localization and Navigation: Theory, Research and Practice. CRC Press, Taylor & Francis Group, 2019.
A fast matrix majorization-projection method for penalized stress minimization with box constraints
IEEE Transactions on Signal Processing, 66(16): 4331-4346, 2018. TSP, Code
A sequential majorization method for approximating weighted time series of finite rank
Statistics and Its Interface, 11 (2018), 615--630.
Iterative Reweighted Methods for l1-lp Minimization
Computational Optimization and Applications, 70 (2018), 201--219.
An inexact smoothing Newton method for Euclidean distance matrix optimization under ordinal constraints
Journal of Computational Mathematics, 35 (2017), 467--483.
A convergent iterative hard thresholding for sparsity and nonnegativity constrained optimization
Pacific Journal of Optimization, 13(2): 325-353, 2017. PJO, RG, Code
Convex Optimization Learning of Faithful Euclidean Distance Representations in Nonlinear Dimensionality Reduction
Mathematical Programming, 164 (2017), 341--381.
Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation
April 2015 (Revised September 2015) (Matlab code: NLOSEDM.zip)
Computational Optimization and Applications, 66 (2017), 187--218.
A Convex Matrix Optimization for the Additive Constant Problem in Multidimensional Scaling with Application to locally linear embedding
(Matlab code for H-weighted case: CENewton_h, need CENewton and CENewton_d)
SIAM J. Optimization, 26-4 (2016), pp. 2564--2590.
Tackling the Flip Ambiguity in Wireless Sensor Network Localization and Beyond
(Matlab code: EDME.zip)
Digital Signal Processing, 55 (2016), pp. 85--97.
A Null-space-based weighted l1 minimization approach to compressed sensing
Information and Inference, 5(1): 76-102, 2016. IMAIAI, RG, Code
Regularized Multidimensional Scaling with Radial Basis Functions
Journal of Industrial Management and Optimization, 12 (2016), pp. 543--563.
Constrained Best Euclidean Distance Embedding on a Sphere: a Matrix Optimization Approach
SIAM J. Optimization, 25 (2015), pp. 439--467.
A Computable Characterization of the Extrinsic Mean of Reflection Shapes and Its Asymptotic Properties
Dedicated to Professor Jiye Han on his 80th birthday.
Asia-Pacific Journal of Operations Research, 32 (2015), 1540005 (16 pages).
Computing the Nearest Euclidean Distance Matrix with Low Embedding Dimensions
(See the Matlab area for the EMBED package used in the paper).
Mathematical Programming, Ser. A (2014) 147:351--389 (DOI: 10.1007/s10107-013-0726-0).
Conditional Quadratic Semidefinite Programming: Examples and Methods
Journal of Operations Research Society of China (2014) 2:143--170
A Lagrangian dual approach to the single source localization problem
(See the Matlab area for the codes used in the paper).
IEEE Transactions on Signal Processing, 61 (2013), 3815--3826.
A semismooth Newton method for the nearest Euclidean distance matrix problem (Matlab code: ENewton.m)
SIAM Journal Matrix Analysis and Applications, 34 (2013), 67--93.
A convex quadratic semidefinite programming approach to the partial additive constant problem in multidimensional scaling (published version)
Journal of Statistical Computation and Simulation, 82 (2012), 1317--1336.
A sequential semismooth Newton method for the nearest low-rank correlation matrix problem (published version)
SIAM Journal on Optimization, Vol 21 (2011), 1641--1666.
A semidefinite programming study of the Elfving theorem
Journal of Statistical Planning and Inference, Vol 141 (2011), 3117--3130.
Block Relaxation and Majorization Methods for the Nearest Correlation Matrix with Factor Structure
Computational Optimization and Applications, Vol 50 (2011), 327--349.
An Augmented Lagrangian Dual Approach for the $H$-Weighted Nearest Correlation Matrix Problem
IMA J. Numerical Analysis, Vol 31 (2011), 491--511
Newton's method for computing the nearest correlation matrix with a simple upper bound
Journal of Optimization Theory and Applications, Vol 147 (2010), 546--568.
Correlation stress testing for value-at-risk: an unconstrained convex optimization approach
Computational Optimization and Applications, vol 45 (2010), 427--462.
Local duality of nonlinear semidefinite programming
Mathematics of Operations Research 34(1), (2009), 124--141.
Positive Semidefinite Matrix Completions on Chordal Graphs and Constraint Nondegeneracy in Semidefinite Programming
Linear Algebra and Its Applications, Vol 430 (2009), 1151--1164.
Data Integration for Recommendation Systems.
In: M.A. Wani, X. Chen, D. Casasent, L. Kurgan, T. Hu, and K. Hafeez, ed. Proceeding of 7th International Conference on Machine Learning and Applications, 2008, 863--866. 7th International Conference on Machine Learning and Applications, DEC 11-13, 2008 San Diego, CA.
Applications of semidefinite programming in XML document classification.
In: M.W. Berry and M. Castellanos, ed. Survey of Text Mining II: Clustering, Classification, and Retrieval. Springer 2008, pp. 129-144.
New sufficient conditoions for global robust stability of delayed neural networks
IEEE Transactions on Circuits and Systems - I: Regular Papers vol. 54, pp. 1131--1141, 2007.
An application of the nearest correlation matrix on Web document classification
Journal of Industrial Mathematics and Optimization, vol. 3, pp. 701--713, 2007
Regularity and well-posedness of a dual program for convex best $C^1$-spline interpolation
Computational Optimzation and Applications, 37, pp. 409--425, 2007.
A quadratically convergent Newton method for computing the nearest correlation matrix
SIAM J. Matrix Analysis and Application vol 28 (2), pp. 360--385, 2006.
Cartesian P-property and its applications to the semidefinite linear complementarity problem
Math. Programming, 2006 (106), pp. 177--201.
Armijo Newton method for convex best interpolation
Optimization Methods and Software, 2006 (21), pp. 179--200.
Deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis II
IEEE Transactions on Neural Networks, 2005 (16), pp. 1701--1706.
Some theoretical aspects on Newton's method for constrained best interpolation
"Continuous Optimization: Current Trends and Modern Applications" (edited by A. Rubinov and V. Jeyakumar), pp. 23--49. Springer (2005).
Smooth convex approximation to the maximum eigenvalue function
J. of Global Optimization, 30 (2004), pp. 253--270.
Semismoothness of spectral functions
SIAM J. Matrix Anal. Appl. 25 (2004), 784--803.
Deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis
IEEE Transactions on Neural Networks, 15 (2004), 99--109.
Neurodynamic optimization
J. of Global Optimization, 28 (2004), 175--195.
Solving KKT systems via the trust region and the conjugate gradient methods
SIAM J. Optimization, 14 (2003), 439--463.
Finite termination of a dual Newton method for convex best $C^1$ interpolation and smoothing
Numerische Mathematik, 96 (2003), 317--337.
Analysis of nonsmooth symmetric-matrix functions with applications to semidefinite complementarity problems
SIAM J. Optimization 13 (2003), pp. 960--985.
Quadratic convergence of Newton's method for convex interpolation and smoothing
Constructive Approximation 19 (2003), pp. 123-143.
A feasible semismooth asympototically Newton method for mixed complementarity problems
Mathematical Programming 94 (2002), pp. 167--187.
On the minimum normal solution of linear programs
Journal of Optimization Theory and Applications, 116 (2003), pp. 333--345.
A Newton method for shape-preserving spline interpolation
SIAM J. Optimization 13 (2002), pp. 588-602.
Quadratic convergence of Newton's method for constrained interpolation
Approximation Theory X: Wavelets, Splines, and Applications, (2002), pp. 261--270.
Charles K. Chui, Larry L. Schumaker, and Joachim Stoeckler (eds.) Vanderbilt University Press, Nashville, TN.
Stability analysis of gradient-based neural network for optimization problems
Journal of Global Optimization, 19 (2001), pp. 363-381.
Solving nonlinear complementarity problems with neural networks: a reformulation method approach
Journal of Computational and Applied Mathematics, 131 (2001), pp. 343-359.
Convergence of Newton's methods for convex best interpolation
Numerische Mathematik, 87 (2001), pp. 435-456.
A new QP-free, globally convergent, locally superlinearly convergent algorithm for inequality constrained optimization
SIAM Journal on Optimization, 11 (2000), pp. 113-132
A smoothing Newton method for general nonlinear complementarity problems
Computational Optimization and Applications, 17 (2000), pp. 231-253.
A globally derivative-free descent method for nonlinear complementarity problems
Journal of Computational Mathematics, 18 (2000), pp. 251-264.
A regularized smoothing Newton method for box constrained variational inequality problems with $P0$-functions
SIAM Journal on Optimization, 10 (2000), pp. 315-330.
A smoothing Newton method for extended vertical linear complementarity problems
SIAM J. Matrix Anal. Appl., 21 (2000), pp. 45-66.
A QP-free constrained Newton-type method for variational inequality problems
Mathematical Programming, 85 (1999), pp. 81-106.
On stationary and minimizing sequences of a new class of merit functions for nonlinear complementarity problems
Journal of Optimization Theory and Applications, 102 (1999), pp. 411--431.
Tikhonov regularization methods for general variational inequality problems
Journal of Optimization Theory and Applications, 102 (1999), pp. 93--101.
A neural network for the linear complementarity problem
Mathematical and Computer Modelling, 29 (1999), pp. 9--18.
Regularized smoothing approximations to vertical nonlinear complementarity problems
Journal of Mathematical Analysis and Applications, 230 (1999), pp. 261--276.
Exceptional families and existence theorems for variational inequality problems
Journal of Optimization Theory and Applications, 101 (1999), pp. 475--495.
A monotone property of the projection operator onto closed convex sets
J. Math. Res. Exposition, 18 (1998), pp. 580--582.
Convergence analysis of a class of conjugate gradient methods without sufficient decrease condition
Acta Math. Sci. (English Ed.), 18 (1998), pp.11-16.
Exceptional family and existence theorems in linear complementarity problems
Mathematica Numerica Sinica, 19 (1997), pp. 70-77.
Modified Hestenes-Stiefel conjugate gradient methods
Chinese Annual of Mathematics, 17 (A) (1996), pp. 277--284.