Existence Results for Noncoercive Mixed Variational Inequalities in Finite Dimensional Spaces

Alfredo Iusem () and Felipe Lara ()
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Alfredo Iusem: Instituto Nacional de Matemática Pura e Aplicada (IMPA)
Felipe Lara: Universidad de Tarapacá

Journal of Optimization Theory and Applications, 2019, vol. 183, issue 1, No 7, 122-138

Abstract: Abstract 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.

Keywords: Asymptotic analysis; Asymptotic functions; Noncoercive optimization; Variational inequalities; Equilibrium problems; 90C25; 90C26; 90C30 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (10)

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DOI: 10.1007/s10957-019-01548-1

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