Banach空间中的一类非光滑齐次优化问题（英文）  

ON SOME NONSMOOTH HOMOGENEOUS OPTIMIZATION PROBLEMS IN BANACH SPACES

作　　者：张娟[1] 李庶民[2] 

机构地区：[1]昆明理工大学津桥学院工学系,云南昆明650106 [2]昆明理工大学数学系,云南昆明650404

出　　处：《数学杂志》2016年第1期55-68,共14页Journal of Mathematics

基　　金：Supported by Scientific Research Foundation of Yunnan Provincial Education Department(2013Y082);Supported by the National Natural Science Foundation of China(11161025)

摘　　要：本文主要研究了一类非光滑齐次优化问题(HOP).通过运用Clarke次微分的广义欧拉恒等式获得了使得(HOP)问题的最优解成为KKT点的充分条件并给出了(HOP)问题与(HOP)问题的KKT点及最优解之间的等价刻画.本文的结果是文[1]中已有结果的推广.文中还举例说明了结果的正确性.In this paper,we mainly consider the nonsmooth homogeneous optimization problem（HOP）.By using the generalized Euler identity for Clarke＇s subdifferential,a sufficient condition for an optimal solution of（HOP） to be a KKT point is obtained.Moreover,we also give an equivalent characterization of KKT points（optimal solutions） of（HOP） and（HOP）,which extend previous ones in[1].Examples are also given to illustrate our results.

关 键 词：Clarke次微分 KKT点 欧拉恒等式 非光滑齐次优化问题 

分 类 号：O177.92[理学—数学]