一类不可微多目标规划的Wolfe型对偶  

Wolfe Duality for a Class of Nondifferentiable Multiobjective Programming

作　　者：赵洁[1] 

机构地区：[1]重庆师范大学涉外商贸学院数学与计算机学院,重庆401520

出　　处：《重庆师范大学学报（自然科学版）》2014年第4期30-36,共7页Journal of Chongqing Normal University:Natural Science

基　　金：重庆市自然科学基金(No.CSTC2012jjA00002);重庆师范大学涉外商贸学院校级科研项目(No.KY2013008)

摘　　要：G-不变凸函数是一类新的广义凸函数,是G-凸函数的推广。本文主要研究了一类带等式和不等式约束的目标函数带支撑函数的不可微多目标规划问题。首先,构造了该问题的Wolfe型对偶模型。其次,利用G-Karush-Kuhn-Tucker最优性必要条件,分别在G-不变凸和G-拉格朗日函数不变凸假设下证明了该问题及其对偶问题的弱对偶定理。最后,在适当条件下给出该问题及其对偶问题的强对偶和逆对偶定理及其证明。本文的结论更具一般性,将前人的相关结论推广到了非可微的情形。A G-invex function is a class of generalized convex functions. It is a generalization of the G-convex functions. In this pa- per, a class of nondifferentiable muhiobjective programs with both inequality and equality constrains in which every component of the objective function contains a term involving the support function of a compact convex set are considered. Wlofe type dual prob- lem is formulated firstly. Furthermore, we use G-Karush-Kuhn-Tucker neeessary optimality conditions to establish weak duality theorems relating the problem and the dual problems under G-invex assumption and invex assumption of G-lagrange function respec- tively. In the final, strong duality theorem and converse duality theorem are established under suitable conditions. The work gener- alized some related results to the nondifferentiable case.

关 键 词：多目标规划 不可微规划 G-不变凸 Wolfe对偶 

分 类 号：O221.6[理学—运筹学与控制论]