择一性与多目标优化

THE ALTERNATIVE AND MULTIOBJECTIVE OPTIMIZATION

众所周知,线性规划和非线性规划理论中的一些主要定理·(例如最优性条件、对偶性和鞍点定理等),可以统一地由关于两组线性不等式相容的择一性定理推导而得.Giannessi 提出,用广义的函数不等式组相容的择一性定理来统一地处理多目标(向量)优化理论中的一些主要定理,但这种推广还不足以处理不可微规划的最优性条件.本文用集值映射的概念提出两组广义不等式系统的择一性。

This paper presents the alternative between two generalized systems of inequalities to deduce necessary and suffucient conditions of nondominated (efficient) solution,duality theorems,sad-dle-point theorems,and generalized Kuhn-Tucker conditions of nonsmooth multi-objective pro-gramming in a unified way.