A note on minimax optimization problems with an infinite number of constraints
Journal of Applied and Numerical Optimization · 2021
In this paper, employing some advanced tools of variational analysis and generalized differentiation, we establish necessary conditions for locally optimal solutions of minimax optimization problems with infinitely many constraints.Sufficient conditions for such solutions to the considered problem are also provided by introducing generalized convex functions defined in terms of the limiting subdifferential for locally Lipschitz functions.In addition, some duality results for minimax optimization problems with infinitely many constraints are also provided.Furthermore, we derive necessary and sufficient conditions for a weak Pareto solution to the multiobjective optimization problem.