summary:In this paper we study set-valued optimization problems with equilibrium constraints (SOPECs) described by parametric generalized equations in the form \[ 0\in G(x)+Q(x), \] where both $G$ and $Q$ are set-valued mappings between infinite-dimensional spaces. Such models particularly arise from certain optimization-related problems governed by set-valued variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish general results on the existence of optimal solutions under appropriate assumptions of the Palais-Smale type and then derive necessary conditions for optimality in the models under consideration by using advanced tools of variational analysis and generalized differentiation.
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机译：摘要：在本文中，我们研究具有均衡约束（SOPEC）的集值优化问题，该问题由参数广义方程描述为\ [0 \ in G（x）+ Q（x），\]，其中$ G $和$ Q $是无穷维空间之间的集值映射。这样的模型尤其来自某些与优化有关的问题，这些问题由不可微分程序设计中的集值变分不等式和一阶最优条件控制。我们在Palais-Smale类型的适当假设下建立关于最优解的存在的一般结果，然后通过使用变分分析和广义微分的先进工具，为正在考虑的模型中的最优性得出必要的条件。
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