【摘要】 目的　研究拓扑向量空间中集值映射优化问题及Lagrangian型对偶问题。方法　将单值映射的广义次类凸概念推广到集值映射,在拓朴向量空间中建立了择一定理,通过择一定理研究集值映射优化问题的最优性必要条件,并定义了Lagrangian型对偶问题。结果　获得了集值映射优化问题的最优性必要条件和对偶定理。结论　其结果深化和丰富了最优化理论的内容。更多还原

【Abstract】 Aim In topological vector spaces, the optimization of set-valued maps and Lagrangian type dual problems are studied.MethodsThe concept of genralized subconvexlikeness of single-valued maps is extended to set-valued maps. An alternative theorem is established in topological vector spaces.Then, an optimality necessary conditon for the optimization of set-valued maps is studied using this alternative theorem. A Lagrangian type dual is defined. ResultsAn optimality necessary condition for the optimization of set-valued maps and duality results are established. ConclusionThese results deepen and enrich content of optimization theory.更多还原