一类多目标非线性规划广义Lagrange对偶函数的几个性质

Some Properties of a Genralized Lagrange Dual Function for a Kind of Multiobjective Nonlinear Programming

本文对多目标非线性规划问题（ＶＰ）：ｍｉｎｆ（ｘ）ｓ．ｔ．β（ｘ）∈－Ｐ，ｘ∈Ｃ引进了一种广义的Ｌａｇｒａｎｇｅ对偶函数Ｑ（ｗ）＝ｉｎｆ｛ｆ（ｘ）＋〈ｗ，β（ｘ）〉｜ｘ∈Ｃ｝，并讨论它的性质，得到了类似文献［１］中的结果．

This paper introduces a type of generalized Lagrange dual function Q(w)= inf {f(x)+〈w, β(x)〉 |x∈C} , for multiobjective nonlinear programming (VP): min f(x) s.t. β(x)∈-P,x∈C. and discusses its properties. We obtain Some conclusions what is similar to that in