非线性规划的非完全Lagrange函数与最优性条件(英文)

Incomplete Lagrange Function and Optimality in Nonlinear Programming

非线性规划问题 (P)“minf(x) subjecttohj(x) 0 ,j =1,2 ,… ,m”的非完全Lagrange函数定义为 L(x ,λJ) =f(x) + (λJ) ThJ(x)其中 ,J { 1,2 ,… ,m}。当J ={ 1,2 ,… ,m } 时 ,它即为通常的Lagrange函数。在一类广义凸意义下考虑非线性规划问题的非完全Lagrange函数及其鞍点最优性条件。在某种意义上 ,本文的结果推广了文[1,2 ,4 ,5] 中的有关结果。

The incomplete Lagrange function of problem (P)'min f(x) subject to h j(x),j=1,2,...,m' is defined by L(x,λ J)=f(x)+(λ J) T h J(x) where J{1,2,...,m}. When J={1,2,...,m}, it is a usual Lagrange function. In this paper, under the assumptions that the involved functions are so called G-(F,ρ), we consider the saddle optimality conditions on the incomplete of Lagrange function of the nonlinear programming. On a certain view, these conditions generalize the some existed results.