Generic Stability and Essential Components of Generalized KKM Points and Applications

We propose the definition of T -KKM points and consider generic stability of T -KKM mappings and essential components of sets of T -KKM points. As applications, using a unified approach, we derive from these results the existence of essential components of solution sets to various optimization-relat...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2011-03, Vol.148 (3), p.488-504
Main Authors: Khanh, P. Q., Quan, N. H.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control
Optimization
Engineering
Equilibrium
Mapping
Mathematics
Mathematics and Statistics
Neighborhoods
Operations Research/Decision Theory
Optimization
Studies
Theorems
Theory of Computation
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Summary:We propose the definition of T -KKM points and consider generic stability of T -KKM mappings and essential components of sets of T -KKM points. As applications, using a unified approach, we derive from these results the existence of essential components of solution sets to various optimization-related problems. We do this in two steps. First, we deduce the corresponding results for variational inclusions, which are new. Then we obtain, as consequences, the existence of essential components of solutions to other problems, which are new or include recent ones in the literature.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-010-9764-4