Solving large-scale sparse semidefinite programs for combinatorial optimization

被引：179
|
作者：
Benson, SJ [3 ]
Ye, YY
Zhang, X
机构：
[1] Univ Iowa, Dept Management Sci, Iowa City, IA 52242 USA
[2] Huazhong Univ Sci & Technol, Sch Mech Engn, Wuhan 430074, Hubei, Peoples R China
[3] Univ Iowa, Computat Optimizat Lab, Iowa City, IA 52242 USA
来源：
SIAM JOURNAL ON OPTIMIZATION | 2000年 / 10卷 / 02期
关键词：
semidefinite programming; dual potential reduction algorithm; maximum cut problem;
D O I：
10.1137/S1052623497328008
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present a dual-scaling interior-point algorithm and show how it exploits the structure and sparsity of some large-scale problems. We solve the positive semidefinite relaxation of combinatorial and quadratic optimization problems subject to boolean constraints. We report the first computational results of interior-point algorithms for approximating maximum cut semidefinite programs with dimension up to 3,000.
引用
收藏
页码：443 / 461
页数：19
相关论文
共 50 条
  • [41] Implementation of a block-decomposition algorithm for solving large-scale conic semidefinite programming problems
    Monteiro, Renato D. C.
    Ortiz, Camilo
    Svaiter, Benar F.
    COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2014, 57 (01) : 45 - 69
  • [42] Hierarchical node method for solving large-scale sparse linear equations in parallel
    Wang, Yongqing
    Liu, Bin
    ACTA MECHANICA SINICA, 2024, 40 (04)
  • [43] Solving Large-Scale Asymmetric Sparse Linear Equations Based On SuperLU Algorithm
    Wang, Pei
    Yang, Xusheng
    Wang, Zhuoyuan
    Li, Lingong
    He, Jichang
    Wang, Qingjie
    FRONTIERS OF MANUFACTURING SCIENCE AND MEASURING TECHNOLOGY, PTS 1-3, 2011, 230-232 : 1355 - +
  • [44] A GaBP-GPU algorithm of solving large-scale sparse linear systems
    Zheng, Hanyuan
    Song, Anping
    Liu, Zhixiang
    Xu, Lei
    Zhang, Wu
    Journal of Information and Computational Science, 2014, 11 (03): : 911 - 921
  • [45] Semidefinite programming in combinatorial optimization
    Michel X. Goemans
    Mathematical Programming, 1997, 79 : 143 - 161
  • [46] Semidefinite programming in combinatorial optimization
    Goemans, MX
    MATHEMATICAL PROGRAMMING, 1997, 79 (1-3) : 143 - 161
  • [47] SOLVING LARGE-SCALE SYSTEMS
    DANTZIG, GB
    OPERATIONS RESEARCH, 1965, S 13 : B156 - &
  • [48] Semidefinite programming and combinatorial optimization
    Rendl, F
    APPLIED NUMERICAL MATHEMATICS, 1999, 29 (03) : 255 - 281
  • [49] Semidefinite programming in combinatorial optimization
    Goemans, Michel X.
    Mathematical Programming, Series B, 1997, 79 (1-3): : 143 - 161
  • [50] Optimization of large-scale truss structures using sparse SAND formulations
    Wang, Qian
    Arora, Jasbir S.
    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2007, 69 (02) : 390 - 407
12345