An estimate of solution set perturbations for a system of linear inequalities

被引：3

作者：

Lotov, AV ^{[1
]}

机构：

[1] RUSSIAN ACAD SCI,CTR COMP,MOSCOW 117964,RUSSIA

来源：

OPTIMIZATION METHODS & SOFTWARE | 1995年 / 6卷 / 01期

关键词：

linear inequalities; solution set; perturbations; Hausdorff distance; Lipschitz continuity; condition number;

D O I：

10.1080/10556789508805622

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

Hausdorff distance between solution sets of original and perturbed linear inequalities systems in real partially ordered Banach space is estimated. The estimation receives a particular simple expression for finite dimensional case. The concept of condition number for solution set of a linear inequalities system is suggested. Explicit expressions of Lipschitz constants are given.

引用

页码：1 / 24

页数：24

共 19 条

[1]

ASHCHEPKOV LT, 1980, ZH VYCHISL MAT MAT F, V20, P510

[2]

DANIEL JW, 1973, NUMER ANAL, V12, P770

[3] ON APPROXIMATE SOLUTIONS OF SYSTEMS OF LINEAR INEQUALITIES [J].

HOFFMAN, AJ .

JOURNAL OF RESEARCH OF THE NATIONAL BUREAU OF STANDARDS, 1952, 49 (04) :263-265

[4]

Lieberman E. R., 1991, MULTIOBJECTIVE PROGR

[5] MULTIPLE OBJECTIVE ANALYSIS OF LONG-TERM DEVELOPMENT STRATEGIES FOR A NATIONAL-ECONOMY [J].

LOTOV, A ;

CHERNYKH, O ;

HELLMAN, O .

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 1992, 56 (02) :210-218

[6] AN ESTIMATE OF THE STABILITY OF A SET OF SOLUTIONS FOR SYSTEMS OF LINEAR EQUALITIES AND INEQUALITIES [J].

LOTOV, AV .

USSR COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 1985, 25 (02) :83-86

[7] AN ESTIMATE OF THE STABILITY AND THE CONDITION NUMBER OF A SET OF SOLUTIONS FOR A SYSTEM OF LINEAR INEQUALITIES [J].

LOTOV, AV .

USSR COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 1984, 24 (06) :104-111

[8]

LOTOV AV, 1989, LECTURE NOTES EC MAT, V337

[9]

LOTOV AV, 1985, ZH VYCHISL MAT MAT F, V25, P451

[10]

LOTOV AV, 1986, ZH VYCHISL MAT MAT F, V26, P323

← 1 2 →