含约束锥类凸集值优化问题强有效点集的连通性

Connectedness of Strong Efficient Solution Set for Set-valued Optimization Problems under Condition of Cone-convexlike with Constraints

集值优化问题是向量优化理论和应用的主要研究领域之一。在集值优化问题中,解集的连通性又是一个非常重要的研究课题,因为它保证了解可连续的移动。在局部凸拓扑线性空间中给出了集值向量优化问题强有效点集的连通性定理。该定理是在可行域为一般非空紧子集、目标映射为锥类凸及约束映射为上半连续的集值映射条件下得到的。本文给出的强有效点集的连通性定理就推广了现有的集值优化问题强有效性有关点集连通性的一些结果。

Set-valued optimization problem is one of the main research fields of vector optimization theory and applications. One of the important research subjects of set-valued optimization problem is to investigate the connectedness properties of the solution set,as it provides a possibility moving from one solution to other solution. In this paper,we present the theorem of the connectedness of strong efficient solution set for set-valued optimization problems in the local convex spaces. The theorem is proved under the condition that the domain is a nonempty compact set and the objective mapping is a cone-convexlike and the constraint mapping is upper semicontinuous set-valued. The obtained theorem in this paper extends the relative results about the connectedness of the strong efficient solution set of vector optimization with set-valued maps.