Kuhn-Tucker Type Optimality Conditions Based on Semi-<i>E</i>-Convex Set-Valued Map Optimization Problem

集值优化是优化理论中的一个重要课题，在经济、管理等领域有着广泛的应用。本文在集值映射的半E-凸性假设下，利用择一定理，建立了集值优化问题的Kuhn-Tucker型最优性充分和必要条件。本文获得的结果推广了文献中的一些已知结果。The set-valued optimization, which is widely applied in fields such as economics and management, is an important topic in optimization theory. In this paper, we will establish Kuhn-Tucker type optimality sufficient and necessary conditions for set-valued optimization problems under the assumption of semi-E-convexity of the set-valued map by using the alternative theorem. The results obtained in this paper extend some known results in the literature.