鲁棒复合凸优化的松弛型Fenchel-Lagrange全对偶及最优性条件  

Relaxed Total Fenchel-Lagrange Duality and Optimality Conditions for the Robust Composite Convex Optimization Problem

作　　者：李星星 田利萍 郑晴慧 

机构地区：[1]吉首大学数学与统计学院,湖南 吉首 [2]怀化学院数学与计算科学学院,湖南 怀化

出　　处：《应用数学进展》2024年第8期4012-4020,共9页Advances in Applied Mathematics

摘　　要：该文在函数不一定下半连续,集合不一定是闭集的条件下,利用函数次微分性质,引进新的约束规范条件,等价刻画了鲁棒复合优化问题的最优性条件以及原问题与其松弛型Fenchel-Lagrange对偶问题之间的全对偶。In the case when the functions are not necessarily lower semicontinuous and the sets are not necessarily closed, by using the properties of subdifferential of functions, we introduce some new weaker constraint qualifications. Under those constraint qualifications, the total duality and optimality condition between the robust composite convex optimization problem and its relaxed Fenchel-Lagrange dual problem are established.

关 键 词：鲁棒复合凸优化问题 约束规范条件 松弛型Fenchel-Lagrange全对偶 最优性条件 

分 类 号：O22[理学—运筹学与控制论]