多目标弧式凸规划最优性的充分条件

Sufficient Optimality Conditions in Multiobjective Arcwise—convex Programming

本文讨论多目标弧式凸规划最优性的充分条件。首先,我们给出在一点弧式拟凸、弧式伪凸的两类函数的概念。并将许多有关拟凸函数和伪凸函数的性质推广到弧式拟凸和弧式伪凸的情形。进而,给出多目标弧式凸规划的局部解为整体的几个充分条件,并建立许多Kuhn-Tucker型的充分条件,同时也给出一些其它的最优性充分条件。

In this paper we discuss sufficient optimality conditions in multiobjective arcwise- convex programming. First we give the concepts of two classes of functions which are arewise quasi-convex or arewise pseudo-convex at a point, and then generalize many properties of quasi-convex functions and pseudo-convex functions to the case of are- wise quasi-convexity and arcwise pseudo-convexity. Several sufficient conditions are ob tained, under which a local Pareto efficient solution is a global Pareto efficient solu- tion for the multiobjective arcwise-convex programming problem, some Kuhn-Tucker type sufficient conditions and other sufficient optimality conditions are also established.