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:
-
- Moerikestrasse 6, D-60320 Frankfurt/Main 1 (Germany)
- 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}
}
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