非光滑优化问题的解集刻画  

Characterizations of the Solution Set for Non-smooth Optimization Problems

作　　者：张雯 龙宪军[1] ZHANG Wen;LONG Xianjun(College of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067

出　　处：《西华师范大学学报（自然科学版）》2021年第1期29-34,共6页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金面上项目(11471059);重庆市基础与前沿研究计划项目(cstc2018jcyjAX0119);重庆市教委科学技术研究重点项目(KJZD-K201900801);重庆工商大学科研团队项目(ZDPTTD201908);重庆工商大学研究生创新型科研项目(yjscxx2020-094-31)。

摘　　要：在一定条件下研究了非光滑优化问题的解集刻画。借助Dini方向导数以及推广的凸函数的相关性质,首先,获得了非光滑优化问题的最优性条件;其次,证明了拉格朗日函数在解集上是常数;最后,在h-伪不变线性函数的假设下获得了非光滑优化问题解集的两个等价性刻画。In this paper,some characterizations of the solution set of non-smooth optimization problems are studied under certain conditions with the aid of Dini directional derivative and the related properties of generalized convex function.Firstly,the optimality condition for the non-smooth optimization problem is obtained and then the Lagrange function is proved to be a constant on the solution set.Finally,two equivalent characterizations of the solution set for non-smooth optimization problems are obtained under the assumption of invariant h-pseudolinear function.

关 键 词：非光滑优化问题 Dini方向导数 h-伪不变凸函数 解集刻画 

分 类 号：O224[理学—运筹学与控制论]