On Implicit Active Constraints in Linear Semi-Infinite Programs with Unbounded Coefficients
- Alicante University, Dep. of Statistics and Operations Research (Spain)
- Universidad Tecnologica de Mixteca, Instituto de Fisica y Matematicas (Mexico)
- UDLA, Dep. of Physics and Mathematics (Mexico)
- Universidad Nacional de Cuyo, Facultad de Ciencias Economicas, Instituto de Ciencias Basicas (Argentina)
The concept of implicit active constraints at a given point provides useful local information about the solution set of linear semi-infinite systems and about the optimal set in linear semi-infinite programming provided the set of gradient vectors of the constraints is bounded, commonly under the additional assumption that there exists some strong Slater point. This paper shows that the mentioned global boundedness condition can be replaced by a weaker local condition (LUB) based on locally active constraints (active in a ball of small radius whose center is some nominal point), providing geometric information about the solution set and Karush-Kuhn-Tucker type conditions for the optimal solution to be strongly unique. The maintaining of the latter property under sufficiently small perturbations of all the data is also analyzed, giving a characterization of its stability with respect to these perturbations in terms of the strong Slater condition, the so-called Extended-Nuernberger condition, and the LUB condition.
- OSTI ID:
- 22043933
- Journal Information:
- Applied Mathematics and Optimization, Vol. 63, Issue 2; Other Information: Copyright (c) 2011 Springer Science+Business Media, LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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