Abstract

The purpose of this paper is to study the characterization of the solution set for nonconvex semi-infinite programming problems related to tangential subdifferentials. We give a necessary optimality condition for the solution set of the nonconvex semi-infinite programming problem. We also prove that the Lagrangian function associated with a fixed Lagrange multiplier is constant on the solution set for semi-infinite programming problems. Finally, by using Dini pseudoconvexity, we obtain two characterizations of the solution set of the problem considered in this paper. Some examples are given to illustrate our results.

中文翻译：

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表征涉及切向子微分的非凸半无限程序的解集

摘要

本文的目的是研究与切向子微分有关的非凸半无限规划问题的解集的特征。我们为非凸半无限规划问题的解集提供了必要的最优性条件。我们还证明，与固定Lagrange乘数关联的Lagrangian函数在半无限编程问题的解集上是恒定的。最后，通过使用Dini伪凸性，我们获得了本文考虑的问题的解集的两个特征。给出了一些例子来说明我们的结果。