广义凸多目标规划的最优性  

On Optimality of Generalized Convex Multi-objective Programming

作　　者：苏紫洋 王荣波[1] SU Ziyang;WANG Rongbo(Yan'an University School of Mathematics and Computer Science,Yan'an Shaanxi 716000,China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《西南师范大学学报（自然科学版）》2021年第11期1-7,共7页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(61861044);延安大学校级科研项目(YDY2019-17);延安大学校级创新项目(YCX2020102).

摘　　要：借助Clarke广义梯度以及凸泛函的相关性质,给出了一些新的广义凸函数:广义(C,α)-Ⅰ型凸函数、广义严格拟(C,α)-Ⅰ型凸函数以及广义严格拟伪(C,α)-Ⅰ型凸函数.在新的广义凸性下,得到了一类多目标规划问题的若干最优性充分条件.With the help of the Clarke generalized gradient and the related properties of convexfunctionals, some generalized convex functions have been given: generalized(C,α)-type Ⅰ convex functions, generalized strict quasi-(C,α)-type Ⅰ convex functions, and generalized strict quasi-pseudo-(C,α)-type Ⅰ convex functions. Under these new generalized convexities, some sufficient condition of optimality for a class of multi-objective programming problems have been obtained.

关 键 词：广义(C α)-I型凸函数 Clarke广义梯度 最优性充分条件 多目标规划 

分 类 号：O221.2[理学—运筹学与控制论]