锥—次类凸向量函数与多目标规划的真有效解

CONE-SUBCONVEXLIKE VECTOR-VALUED FUNCTIONS AND PROPERLY EFFICIENT SOLUTIONS IN MULTIOBJECTIVE PROGRAMMING

首先在锥—次类凸性假设下证明几种真有效解的概念彼此等价,然后建立多目标规划真有效解的标量化定理、Lagrange乘子定理、鞍点定理、Lagrange对偶定理和广义Kuhn-Tucker定理等。这些定理改进或推广了关于真有效解已有的一些结果。

It is showed that several types of properly efficient solutionsare equivalent under an assumption of the cone-subconvexlikeness. Based on this result, a scalarization theorem, a Lagrange multiplier theorem, a saddle point theorem, two Lagrange duality theorems and a generalized Kuhn-Tucker theorem for a properly efficient solution in multiobjective programming are established.