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We show that Malitsky’s recent Golden Ratio Algorithm for solving convex mixed variational inequalities can be employed in a certain nonconvex framework as well, making it probably the first iterative method in the literature for solving generalized convex mixed variational inequalities, and illustrate this result by numerical experiments.

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We use asymptotic analysis for studying noncoercive pseudomonotone equilibrium problems and vector equilibrium problems. We introduce suitable notions of asymptotic functions, which provide sufficient conditions for the set of solutions of these problems to be nonempty and compact under quasiconvexity of the objective function. We characterize the efficient and weakly efficient solution set for the nonconvex vector equilibrium problem via scalarization. A sufficient condition for the closedness of the image of a nonempty, closed and convex set via a quasiconvex vector-valued function is given. Finally, applications to the quadratic fractional programming problem are also presented.