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Title: Regions of stability for ill-posed convex programs (English)
Author: Zlobec, Sanjo
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 27
Issue: 3
Year: 1982
Pages: 176-191
Summary lang: English
Summary lang: Czech
Summary lang: Russian
Category: math
Summary: Regions of stability are chunks of the space of parameters in which the optimal solution and the optimal value depend continuously on the data. In these regions the problem of solving an arbitrary convex program is a continuous process and Tihonov's regularization is possible. This paper introduces a new region we furnisch formulas for the marginal value. The importance of the regions of stability is demostrated on multicriteria decision making problems and in calculating the minimal index set of binding constraints in convex programming. These two nonlinear problems can be reduced to calculating a region of stability for a simple linear program. If Slater's condition holds, or for the rihgt hand side perurbations, the results reduce to the familiar ones. (English)
Keyword: ill-posed convex programs
Keyword: regions of stability
Keyword: Tihonov’s regularization
Keyword: formulas for the marginal value
Keyword: multicriteria decision making
Keyword: minimal index set of binding constraints
MSC: 90C25
MSC: 90C31
idZBL: Zbl 0482.90073
idMR: MR0658001
Date available: 2008-05-20T18:19:10Z
Last updated: 2015-07-08
Stable URL:
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