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

Unicity Results for General Linear Semi-Infinite Optimization Problems Using a New Concept of... Abstract. We consider parametric semi-infinite optimization problems without the usual asssumptions 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 pertubations. This result generalizes a well-known theorem of Nürnberger. 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

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

Applied Mathematics and Optimization , Volume 38 (1): 23 – Aug 1, 1998

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References (12)

Publisher
Springer Journals
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s002459900080
Publisher site
See Article on Publisher Site

Abstract

Abstract. We consider parametric semi-infinite optimization problems without the usual asssumptions 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 pertubations. This result generalizes a well-known theorem of Nürnberger. 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.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Aug 1, 1998

Keywords: Key words. Semi-infinite linear optimization, Parametric optimization, Density of the unicity set, Strong unicity. AMS Classification. 90C05, 90C34, 65K05, 49M39.

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