This paper is concerned with the study of optimality conditions for minimax optimization problems with an infinite number of constraints, denoted by (MMOP). More precisely, we first establish necessary conditions for optimal solutions to the problem (MMOP) by means of employing some advanced tools of variational analysis and generalized differentiation. Then, sufficient conditions for the existence of such solutions to the problem (MMOP) are investigated with the help of generalized convexity functions defined in terms of the limiting subdifferential of locally Lipschitz functions. Finally, some of the obtained results are applied to formulating optimality conditions for weakly efficient solutions to a related multiobjective optimization problem with an infinite number of constraints, and a necessary optimality condition for a quasi ε-solution to problem (MMOP).

本文涉及具有无限数量约束的极小极大优化问题的最优条件的研究，用（MMOP）表示。更准确地说，我们首先通过使用一些先进的变分分析和广义微分工具，为问题的最佳解决方案（MMOP）建立必要的条件。然后，借助根据局部Lipschitz函数的极限次微分定义的广义凸函数，研究了解决此类问题（MMOP）的充分条件。最后，将所获得的一些结果应用于为无穷多个约束的相关多目标优化问题的弱有效解制定最优性条件，并为拟似条件提供了必要的最优性条件。ε-问题解决方案（MMOP）。