一类广义路拟凸映射解集的连通性

The Connectedness of the Solutions Sets to a Parameter Path Quasiconvex Mapping

本文介绍了一类广义路拟凸映射的概念。在约束集是紧路连通条件下,目标函数是连续逐点路拟凸时,弱有效解集是连通的。当目标函数是连续严格逐点路拟凸时,有效解集不但连通,而且道路连通。

In this paper, the Concepts of the path quasiconvex, pointwise path quasiconvex and strictly pointwise path quasiconvex are introduced. Under the conditions that the constraint set is compact and path connected, while the objective function is continuous and pointwise path quasiconvex, then the weakly efficient solution set is connected, and when the objective function is continuous and strictly pointwise path quasiconvex, then the efficient salution set not ohly is connected, but also is path connected.