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Existence Results for Noncoercive Mixed Variational Inequalities in Finite Dimensional Spaces

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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.

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Acknowledgements

The authors want to express their gratitude to both referees for their criticism and suggestions that helped to improve this paper. For the second author, this research was partially supported by Conicyt-Chile throughout Fondecyt Iniciación 11180320.

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Authors and Affiliations

  1. Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, Brazil

    Alfredo Iusem

  2. Departamento de Matemáticas, Universidad de Tarapacá, Arica, Chile

    Felipe Lara

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  1. Alfredo Iusem
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  2. Felipe Lara
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Correspondence to Felipe Lara.

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Iusem, A., Lara, F. Existence Results for Noncoercive Mixed Variational Inequalities in Finite Dimensional Spaces. J Optim Theory Appl 183, 122–138 (2019). https://doi.org/10.1007/s10957-019-01548-1

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  • DOI: https://doi.org/10.1007/s10957-019-01548-1

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