Simplex-like trajectories on quasi-polyhedral sets

被引：12

作者：

Anderson, EJ ^{[1
]}

Goberna, MA

López, MA

机构：

[1] Univ New S Wales, Australian Grad Sch Management, Sydney, NSW 2052, Australia

[2] Univ Alicante, Fac Sci, Dept Stat & Operat Res, Alicante 03071, Spain

来源：

MATHEMATICS OF OPERATIONS RESEARCH | 2001年 / 26卷 / 01期

关键词：

semi-infinite programming; simplex-like algorithms; locally polyhedral systems; quasi-polyhedral sets;

D O I：

10.1287/moor.26.1.147.10595

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：

This paper presents a unified treatment of two new simplex-like methods for linear semi-infinite programming problems with quasi-polyhedral feasible sets. The simplex method combines a purification phase I (which provides an extreme point from a given Feasible solution) with the iterative application of a pivot operation, yielding a trajectory which consists of a (possibly infinite) sequence of linked edges (phase II). The reduced gradient method also consists of two phases and it can be applied even when the Feasible set has no extreme point.

引用

页码：147 / 162

页数：16

共 20 条

[1] AN EXTENSION OF THE SIMPLEX ALGORITHM FOR SEMI-INFINITE LINEAR-PROGRAMMING
ANDERSON, EJ
LEWIS, AS
[J]. MATHEMATICAL PROGRAMMING, 1989, 44 (03) : 247 - 269
[2] Anderson EJ, 1998, LINEAR ALGEBRA APPL, V270, P231
[3] Anderson EJ, 1987, LINEAR PROGRAMMING I
[4] [Anonymous], 1985, FINITE ALGORITHMS OP
[5] BLUM E, 1975, MATH OPTIMIERUNG
[6] CARASSO C, 1973, THESIS U GRENOBLE GR
[7] Gill P. E., 1973, Linear Algebra and Its Applications, V7, P99, DOI 10.1016/0024-3795(73)90047-5
[8] GLASHOFF K, 1983, LINEAR OPTIMIZAITON
[9] OPTIMALITY THEORY FOR SEMIINFINITE LINEAR-PROGRAMMING
GOBERNA, MA
LOPEZ, MA
[J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 1995, 16 (5-6) : 669 - 700
[10] Goberna MA., 1998, LINEAR SEMIINFINITE

← 1 2 →