Regions of stability for ill-posed convex programs

Sanjo Zlobec

Aplikace matematiky (1982)

  • Volume: 27, Issue: 3, page 176-191
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Zlobec, Sanjo. "Regions of stability for ill-posed convex programs." Aplikace matematiky 27.3 (1982): 176-191. <http://eudml.org/doc/15238>.

@article{Zlobec1982,
abstract = {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.},
author = {Zlobec, Sanjo},
journal = {Aplikace matematiky},
keywords = {ill-posed convex programs; regions of stability; Tihonov’s regularization; formulas for the marginal value; multicriteria decision making; minimal index set of binding constraints; ill-posed convex programs; regions of stability; Tihonov's regularization; formulas for the marginal value; multicriteria decision making; minimal index set of binding constraints},
language = {eng},
number = {3},
pages = {176-191},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Regions of stability for ill-posed convex programs},
url = {http://eudml.org/doc/15238},
volume = {27},
year = {1982},
}

TY - JOUR
AU - Zlobec, Sanjo
TI - Regions of stability for ill-posed convex programs
JO - Aplikace matematiky
PY - 1982
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 27
IS - 3
SP - 176
EP - 191
AB - 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.
LA - eng
KW - ill-posed convex programs; regions of stability; Tihonov’s regularization; formulas for the marginal value; multicriteria decision making; minimal index set of binding constraints; ill-posed convex programs; regions of stability; Tihonov's regularization; formulas for the marginal value; multicriteria decision making; minimal index set of binding constraints
UR - http://eudml.org/doc/15238
ER -

References

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