在约束条件下集值全局真有效点集的连通性

The Connectedness of Globally Proper Effective Set of Set-valued Points under Constraint Conditions

讨论全局真有效点集在局部凸拓扑线性空间中的连通性。在可行域为非空的一般紧子集、约束集上的目标集值映射是上半连续且为锥类凸的、约束映射为上半连续的情况下,通过对对偶锥上的集值映射连通性的证明,给出了含约束锥类凸的集值优化问题全局有效点集的非空连通性定理。此结论是在相对较弱的条件下得到的,这就使目前的全局真有效点集连通性的相关结论得到了进一步拓展。

Discuss globally proper effective point sets connectivity in locally convex topological linear space.In the case that the feasible domain is a general compact subset that is non-empty,the target set value mapping on the constraint set is upper semicontinuous and cone-like convex,and the constraint mapping is upper semi-continuous.By proving the connectedness of set-valued maps on dual cones,a nonempty connectivity theorem for global effective point set for set-valued optimization problems with constrained cone-like convex is presented.This conclusion is obtained under relatively weak conditions,which further expands the current related conclusions on connectivity of global true efficient point sets.