An alternating direction method for solving convex nonlinear semidefinite programming problems

被引:15
|
作者
Zhang, Su [1 ]
Ang, James [2 ]
Sun, Jie [2 ,3 ]
机构
[1] Nankai Univ, Inst Modern Management, Sch Business, Tianjin, Peoples R China
[2] Natl Univ Singapore, Dept Decis Sci, Singapore 119245, Singapore
[3] Natl Univ Singapore, Risk Management Inst, Singapore 119245, Singapore
关键词
alternating direction method; convex semidefinite programming; matrix completion; variational inequalities; 65L20; 65K10; 90C25; MAXIMUM EIGENVALUE FUNCTIONS; SMOOTHING NEWTON METHOD; SPECTRAL BUNDLE METHODS; CUTTING PLANE METHOD; P-PROPERTIES; OPTIMIZATION;
D O I
10.1080/02331934.2011.611883
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
An alternating direction method is proposed for solving convex semidefinite optimization problems. This method only computes several metric projections at each iteration. Convergence analysis is presented and numerical experiments in solving matrix completion problems are reported.
引用
收藏
页码:527 / 543
页数:17
相关论文
共 50 条
  • [1] Solving semidefinite programming problems via alternating direction methods
    Yu, Zhensheng
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2006, 193 (02) : 437 - 445
  • [2] Modified alternating direction method of multipliers for convex quadratic semidefinite programming
    Chang, Xiaokai
    Liu, Sanyang
    Li, Xu
    NEUROCOMPUTING, 2016, 214 : 575 - 586
  • [3] Alternating Direction Method Of Solving Nonlinear Programming With Inequality Constrained
    Feng, Aifen
    Zhang, Liming
    Xue, Zhenxia
    MATERIAL SCIENCE, CIVIL ENGINEERING AND ARCHITECTURE SCIENCE, MECHANICAL ENGINEERING AND MANUFACTURING TECHNOLOGY II, 2014, 651-653 : 2107 - +
  • [4] Solving generalized convex multiobjective programming problems by a normal direction method
    Tran Ngoc Thang
    Dinh The Luc
    Nguyen Thi Bach Kim
    OPTIMIZATION, 2016, 65 (12) : 2269 - 2292
  • [5] The Alternating Direction Search Pattern Method for Solving Constrained Nonlinear Optimization Problems
    Feng, Aifen
    Chang, Xiaogai
    Shang, Youlin
    Fan, Jingya
    MATHEMATICS, 2023, 11 (08)
  • [6] SOLVING LARGE-SCALE LEAST SQUARES SEMIDEFINITE PROGRAMMING BY ALTERNATING DIRECTION METHODS
    He, Bingsheng
    Xu, Minghua
    Yuan, Xiaoming
    SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2011, 32 (01) : 136 - 152
  • [7] A modified alternating direction method for convex minimization problems
    He, BS
    Zhou, J
    APPLIED MATHEMATICS LETTERS, 2000, 13 (02) : 123 - 130
  • [8] A modified alternating direction method for convex quadratically constrained quadratic semidefinite programs
    Sun, Jie
    Zhang, Su
    EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 2010, 207 (03) : 1210 - 1220
  • [9] Optimally linearizing the alternating direction method of multipliers for convex programming
    He, Bingsheng
    Ma, Feng
    Yuan, Xiaoming
    COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2020, 75 (02) : 361 - 388
  • [10] Optimally linearizing the alternating direction method of multipliers for convex programming
    Bingsheng He
    Feng Ma
    Xiaoming Yuan
    Computational Optimization and Applications, 2020, 75 : 361 - 388