半拟可微拟凸规划的KKT型最优性条件  

Karush-Kuhn-Tucker Type Optimality Conditions for Semi-quasi-differentiable Quasi-convex Programming

作　　者：何坤 郭洋俊骁 赵世莲[1] HE Kun;GUO Yang-jun-xiao;ZHAO Shi-lian(School of Mathematics and Information,China West Normal University,Nanchong Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2024年第2期150-154,共5页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(11871059)。

摘　　要：最优性条件在优化问题中起着重要的作用,它为优化算法的研究提供了重要的理论依据。众所周知,凸规划方面最优性条件已比较完善。然而,由于拟凸函数性质的特殊性,对于拟凸规划问题解的Karush-Kuhn-Tucker(KKT)类型最优性条件的研究相对较少。本文利用半拟可微刻画了拟凸规划的最优性条件,同时研究了可行集法锥与带半拟可微性质的约束函数之间的关系,并证明了上述两个结果与Greenberg-Pierskalla次微分的关系。As optimality condition plays an important role in the optimization problem,it provides an important theoretical basis for the study of optimization algorithm.It is well known that the optimality condition of convex programming has been relatively perfect.However,there are only few studies on Karush-Kuhn-Tucker type optimality conditions for the solutions of quasi-convex programming problems due to the special nature of quasi-convex functions.In this paper,the optimality conditions of quasi-convex programming are characterized by semi-quasi-differentiable,and the relationship between the feasible set normal cone and the constraint function with semi-quasi-differentiable properties is studied as well.In addition,the relationship between the above two results and Greenberg-Pierskalla subdifferential is proved.

关 键 词：半拟可微 次微分 拟凸规划 最优性条件 法锥 

分 类 号：O224[理学—运筹学与控制论]