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On Nonconvex Pseudomonotone Equilibrium Problems with Applications

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In this paper, we provide a further study for nonconvex pseudomonotone equilibrium problems and nonconvex mixed variational inequalities by using global directional derivatives. We provide finer necessary and sufficient optimality conditions for both problems in the pseudomonotone case and, as a consequence, a characterization for a point to be a solution for nonconvex equilibrium problems is given. Finally, we apply the golden ratio algorithm for a class of nonconvex functions in equilibrium problems and mixed variational inequalities.

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The author wishes to thank to the associated editor and the reviewers for their corrections and pertinent remarks that contributed to the improvement of the paper. This research was partially supported by Conicyt–Chile under project Fondecyt Iniciación 11180320 and by Universidad de Tarapacá under Project UTAMayor 4749-20.

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Correspondence to F. Lara.

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Lara, F. On Nonconvex Pseudomonotone Equilibrium Problems with Applications. Set-Valued Var. Anal 30, 355–372 (2022).

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