Two-phase simplex method for linear semidefinite optimization

被引：3

作者：

Zhadan, Vitaly ^{[1
]}

机构：

[1] Russian Acad Sci, Dorodnicyn Comp Ctr, FRC Comp Sci & Control, Vaviliva Str 40, Moscow 119333, Russia

来源：

OPTIMIZATION LETTERS | 2019年 / 13卷 / 08期

基金：

俄罗斯基础研究基金会;

关键词：

Linear semidefinite programming; Extreme points; Primal simplex method; Two-phase method; Local convergence;

D O I：

10.1007/s11590-018-1333-z

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：

The linear semidefinite programming problem is considered. To solve it, the variant of the primal simplex method, that generalizes the corresponding method for linear programming problems, is proposed. The passage from one extreme point of the feasible set to another one is described. The main attention is given to pivoting in the case, when the extreme point is irregular, i.e. the "triangular" number of rank of the matrix in the basic point is less than number of equality type constraints in the problem. The approach for finding a starting extreme point is proposed too. The local convergence of the method is proven.

引用

页码：1969 / 1984

页数：16

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