一类半无限规划的鞍点条件

Saddle-Point Condition of a Class of Semi-Infinite Programming

半无限规划是指约束条件有无限多个的一类规划。利用一类B-(p,r,a)不变凸函数,研究了非光滑半无限规划的鞍点问题,得到了当不完全Lagrange函数为非光滑B-(p,r,a)伪不变凸函数、约束函数为B-(p,r,a)拟不变凸函数时,鞍点充分性条件,把已有文献中可微、有限约束条件的鞍点结论推广到非光滑、无限约束条件的情形,在新的凸性下得到一些重要结果。

Semi-infinite programming is a programming whose constraint functions are infinite, by a class of B-（p,r,a） invex func- tions, saddle-point problem of nonsmooth semi-infinite programming involving these functions were researched, saddle-point suffi- cient conditions were obtained when incomplete Lagrange function was B-（p, r, a） pseudo invex functions and the constraint func- tions were B-（p, r,a） quasi invex functions, saddle-point conlusions were extended from differentiable, finite constraint conditions in existed literature to nonsmooth, infinite constraint conditions, many important results were obtained under new convexity.