集值映射多目标半定规划问题的epsilon-弱有效性

对于集值映射多目标半定规划问题, 在近似锥-次类凸的框架下, 建立了含矩阵和向量的择一性定理, 给出了问题的epsilon-弱有效解的epsilon-Lagrange乘子定理及标量化定理和epsilon-弱鞍点定理．     

含参广义集值强向量平衡问题的稳定性

本文借助集合极限的性质和弱f-性假设证明了含参广义集值强向量平衡问题解集映射的下半连续性,其方法不同于最近文献(Zhao,2016和Meng,2018).此外,建立了含参广义集值强向量平衡问题解集连通性的充分条件,并举例验证了所得结果的正确性.本文得结果推广和改进了已有文献(Gong,2008,Xu,2009,Chen,2010,Xu,2013和Zhao,2013)中相应结果.     

基于拟相对内部集值优化问题弱有效元的最优性条件

本文研究了基于拟相对内部的非凸集值优化问题弱有效元的最优性条件.首先,讨论了弱有效元与线性子空间之间的关系,利用涉及拟相对内部的凸集分离定理,获得了弱有效元的最优性条件.其次,给出了基于拟相对内部弱有效元的Lagrange乘子定理.     

Projected subgradient method for non-Lipschitz set-valued mixed variational inequalities

A projected subgradient method for solving a class of set-valued mixed variational inequalities (SMVIs) is proposed when the mapping is not necessarily Lipschitz. Under some suitable conditions, it can be proven that the sequence generated by the method can strongly converge to the unique solution to the problem in the Hilbert spaces.     

锥方向高阶广义邻近导数及高阶Mond-Weir对偶(英文)

本文引入了集值映射的锥方向的高阶广义邻近导数.应用这种导数,构建了约束的集值优化问题的一种高阶Mond-Weir型对偶,并建立了相应的弱对偶,强对偶和逆对偶性,获得的结果推广了文献中的相应结论.     

集值映射的对称向量拟均衡问题

研究向量集值映射的拟均衡问题的有效解,利用数值化方法与不动点定理,得到解的存在性定理.作为应用,得到广义向量鞍点,向量变分不等式与向量互补问题的存在性定理.     

On some Fermat rules for set-valued optimization problems

The aim of this article is to obtain necessary optimality conditions for Pareto minima in set-valued optimization problems. We employ a new method to derive generalized Fermat rules for set-valued optimization. This method is based on openness results for multifunctions and allows recovery of a large number of results and, at the same time, getting several new ones.     

Extended radial epiderivatives of non-convex vector-valued maps and parametric quasiconvex programming

In this paper, we consider extended vector-valued mappings defined on a normed linear space. Based on the recent semicontinuous regularizations related to hypographical and/or epigraphical profile mappings of the considered function introduced, we define semicontinuous radial epiderivatives. We, then, demonstrate that the properties of these epiderivatives amount to properties of hypographical and/or epigraphical profile mappings of the corresponding difference quotient of the underlying function, which simplify fairly well the proofs in the radial epiderivative formulaes. In particular, we stress the impact of semicontinuity, hence, we characterize with new arguments the radial epiderivatives in terms of the suprema and/or infima of the interiorly radial cone of the hypograph and/or epigraph of the considered function. Finally, we obtain optimality conditions for general non-convex constrained vector optimization problems. We apply thereafter the obtained pattern to a parametric quasiconvex programming problem for which we derive necessary and sufficient optimality conditions that are not sensitive to perturbation at the nominal level, yielding henceforth more – and strong at least under asymptotically regular constraints – information than the recent stability results obtained under additional conditions on the regularity of the normal cone to the adjusted sublevel sets of the underlying function.     

集值优化问题的Benson次梯度及其应用

引进集值映射的Benson次梯度,证明Benson次梯度的存在性定理,给出了它的等价刻画。作为应用,给出了带约束集值优化问题取得Benson真有效元的充分条件和必要条件,得到了集值优化问题在Benson真有效意义下的若干新刻画。     

Nonempty intersection theorems and system of generalized vector equilibrium problems in product G-convex spaces

By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.