A study of search directions in primal-dual interior-point methods for semidefinite programming

被引：65
|
作者：
Todd, MJ [1 ]
机构：
[1] Cornell Univ, Sch Operat Res & Ind Engn, Ithaca, NY 14853 USA
来源：
OPTIMIZATION METHODS & SOFTWARE | 1999年 / 11-2卷 / 1-4期
关键词：
semidefinite programming; search direction; invariance properties;
D O I：
10.1080/10556789908805745
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
We discuss several different search directions which can be used in primal-dual interior-point methods for semidefinite programming problems and investigate their theoretical properties, including scale invariance, primal-dual symmetry, and whether they always generate well-defined directions. Among the directions satisfying all but at most two of these desirable properties are the Alizadeh-Haeberly-Overton, Helmberg-Rendl-Vanderbei-Wolkowicz/Kojima-Shindoh-Hara/Monteiro, Nesterov-Todd, Gu, and Toh directions, as well as directions we will call the MTW and Half directions. The first five of these appear to be the best in our limited computational testing also.
引用
收藏
页码：1 / 46
页数：46
相关论文
共 50 条
  • [1] SEMIDEFINITE PROGRAMMING: FORMULATIONS AND PRIMAL-DUAL INTERIOR-POINT METHODS
    Fukuda, Mituhiro
    Nakata, Maho
    Yamashita, Makoto
    [J]. REDUCED-DENSITY-MATRIX MECHANICS - WITH APPLICATION TO MANY-ELECTRON ATOMS AND MOLECULES, 2007, 134 : 103 - 118
  • [2] Exploiting sparsity in primal-dual interior-point methods for semidefinite programming
    Katsuki Fujisawa
    Masakazu Kojima
    Kazuhide Nakata
    [J]. Mathematical Programming, 1997, 79 : 235 - 253
  • [3] Primal-dual interior-point methods for semidefinite programming in finite precision
    Gu, M
    [J]. SIAM JOURNAL ON OPTIMIZATION, 2000, 10 (02) : 462 - 502
  • [4] Some new search directions for primal-dual interior point methods in semidefinite programming
    Toh, KC
    [J]. SIAM JOURNAL ON OPTIMIZATION, 2000, 11 (01) : 223 - 242
  • [5] Structured Primal-dual Interior-point Methods for Banded Semidefinite Programming
    Deng, Zhiming
    Gu, Ming
    Overton, Michael L.
    [J]. TOPICS IN OPERATOR THEORY: OPERATORS, MATRICES AND ANALYTIC FUNCTIONS, VOL 1, 2010, 202 : 111 - +
  • [6] Exploiting sparsity in primal-dual interior-point methods for semidefinite programming
    Fujisawa, K
    Kojima, M
    Nakata, K
    [J]. MATHEMATICAL PROGRAMMING, 1997, 79 (1-3) : 235 - 253
  • [7] A primal-dual interior-point algorithm with arc-search for semidefinite programming
    Zhang, Mingwang
    Yuan, Beibei
    Zhou, Yiyuan
    Luo, Xiaoyu
    Huang, Zhengwei
    [J]. OPTIMIZATION LETTERS, 2019, 13 (05) : 1157 - 1175
  • [8] A primal-dual interior-point algorithm with arc-search for semidefinite programming
    Mingwang Zhang
    Beibei Yuan
    Yiyuan Zhou
    Xiaoyu Luo
    Zhengwei Huang
    [J]. Optimization Letters, 2019, 13 : 1157 - 1175
  • [9] A primal-dual regularized interior-point method for semidefinite programming
    Dehghani, A.
    Goffin, J. -L.
    Orban, D.
    [J]. OPTIMIZATION METHODS & SOFTWARE, 2017, 32 (01): : 193 - 219
  • [10] Monotonicity of primal-dual interior-point algorithms for semidefinite programming problems
    Kojima, M
    Tunçel, L
    [J]. OPTIMIZATION METHODS & SOFTWARE, 1998, 10 (02): : 275 - 296
12345