Existence Results for Noncoercive Mixed Variational Inequalities in Finite Dimensional Spaces

We use asymptotic analysis and generalized asymptotic functions for studying nonlinear and noncoercive mixed variational inequalities in finite dimensional spaces in the nonconvex case, that is, when the operator is nonlinear and noncoercive and the function is nonconvex and noncoercive. We provide...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2019-10, Vol.183 (1), p.122-138
Main Authors: Iusem, Alfredo, Lara, Felipe
Format: Article
Language:English
Subjects:
Applications of Mathematics
Asymptotic properties
Calculus of Variations and Optimal Control
Optimization
Engineering
Inequalities
Mathematical programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Operators (mathematics)
Optimization
Theory of Computation
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Summary:We use asymptotic analysis and generalized asymptotic functions for studying nonlinear and noncoercive mixed variational inequalities in finite dimensional spaces in the nonconvex case, that is, when the operator is nonlinear and noncoercive and the function is nonconvex and noncoercive. We provide general necessary and sufficient optimality conditions for the set of solutions to be nonempty and compact. As a consequence, a characterization of the nonemptiness and compactness of the solution set, when the operator is affine and the function is convex, is given. Finally, a comparison with existence results for equilibrium problems is presented.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-019-01548-1