G_(b)-(p,r)E-半预不变凸多目标规划的最优性条件  

Optimality conditions involving G_(b)(p,r)E semi-pre-invex multi-objective programming

作　　者：祁钰 高晓艳[1] QI Yu;GAO Xiaoyan(College of Science,Xi an University of Science and Technology,Xi an 710600,China)

机构地区：[1]西安科技大学理学院,陕西西安710600

出　　处：《广西大学学报（自然科学版）》2023年第2期487-494,共8页Journal of Guangxi University（Natural Science Edition）

基　　金：国家自然科学基金项目(12001420)

摘　　要：为了丰富广义凸函数类,扩大多目标规划的应用范围,运用Clark广义梯度,借助αE半预不变凸函数和G B(p,r,α)不变凸函数,进一步给出了一类新的广义凸函数的定义:G_(b)(p,r)E半预不变凸函数。对于涉及这类函数的多目标规划问题,得到了其可行解是弱有效解的若干最优性条件。In an effort to develop the classes of generalized convex functions and enlarge the applying range of multi-objective programming,a new type of generalized convex functions,namely G_(b)(p,r)E semi-pre-invex functions,were defined by using Clark generalized gradient on the basis ofαE semi-pre-invex functions and G B(p,r,α)invex functions.Several optimality conditions that the feasible solutions are weakly efficient solutions of multi-objective programming problems involving this kind of functions are studied.

关 键 词：G_(b)(p r)E半预不变凸函数 最优性条件 多目标规划 弱有效解 

分 类 号：O221.6[理学—运筹学与控制论] O224[理学—数学]