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Title: Unicity Results for General Linear Semi-Infinite Optimization Problems Using a New Concept of Active Constraints

Abstract

We consider parametric semi-infinite optimization problems without the usual assumptions on the continuity of the involved mappings and on the compactness of the index set counting the inequalities. We establish a characterization of those optimization problems which have a unique or strongly unique solution and which are stable under small perturbations. This result generalizes a well-known theorem of Nuernberger. The crucial roles in our investigations are a new concept of active constraints, a generalized Slater's condition, and a Kuhn-Tucker-type theorem. Finally, we give some applications in vector optimization, for approximation problems in normed spaces, and in the stability of the minimal value.

Authors:
 [1];  [2]
  1. Moerikestrasse 6, D-60320 Frankfurt/Main 1 (Germany)
  2. Bulgarian Academy of Sciences, Institute of Mathematics, 29 Ph. Macedonsky Street, 4002 Plovdiv (Bulgaria)
Publication Date:
OSTI Identifier:
21067569
Resource Type:
Journal Article
Journal Name:
Applied Mathematics and Optimization
Additional Journal Information:
Journal Volume: 38; Journal Issue: 1; Other Information: DOI: 10.1007/s002459900080; Copyright (c) 1998 Springer-Verlag New York Inc.; Article Copyright (c) Inc. 1998 Springer-Verlag New York; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0095-4616
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; MAPPING; MATHEMATICAL SOLUTIONS; MATHEMATICAL SPACE; OPTIMIZATION; STABILITY; VECTORS

Citation Formats

Helbig, S, and Todorov, M I. Unicity Results for General Linear Semi-Infinite Optimization Problems Using a New Concept of Active Constraints. United States: N. p., 1998. Web. doi:10.1007/S002459900080.
Helbig, S, & Todorov, M I. Unicity Results for General Linear Semi-Infinite Optimization Problems Using a New Concept of Active Constraints. United States. https://doi.org/10.1007/S002459900080
Helbig, S, and Todorov, M I. 1998. "Unicity Results for General Linear Semi-Infinite Optimization Problems Using a New Concept of Active Constraints". United States. https://doi.org/10.1007/S002459900080.
@article{osti_21067569,
title = {Unicity Results for General Linear Semi-Infinite Optimization Problems Using a New Concept of Active Constraints},
author = {Helbig, S and Todorov, M I},
abstractNote = {We consider parametric semi-infinite optimization problems without the usual assumptions on the continuity of the involved mappings and on the compactness of the index set counting the inequalities. We establish a characterization of those optimization problems which have a unique or strongly unique solution and which are stable under small perturbations. This result generalizes a well-known theorem of Nuernberger. The crucial roles in our investigations are a new concept of active constraints, a generalized Slater's condition, and a Kuhn-Tucker-type theorem. Finally, we give some applications in vector optimization, for approximation problems in normed spaces, and in the stability of the minimal value.},
doi = {10.1007/S002459900080},
url = {https://www.osti.gov/biblio/21067569}, journal = {Applied Mathematics and Optimization},
issn = {0095-4616},
number = 1,
volume = 38,
place = {United States},
year = {Wed Jul 15 00:00:00 EDT 1998},
month = {Wed Jul 15 00:00:00 EDT 1998}
}