Exhauster广义凸函数及其在非光滑规划中的应用  

Generalized Convex Functions via Exhausters and Their Applications in Nonsmooth Programming

作　　者：祝航召 李晓锋[1] ZHU Hangzhao LI Xiaofeng(College of Mathematics, Jilin University, Changchun 130012, China)

机构地区：[1]吉林大学数学学院,长春130012

出　　处：《吉林大学学报（理学版）》2017年第5期1170-1172,共3页Journal of Jilin University:Science Edition

摘　　要：利用次微分Exhauster定义一类新的广义凸函数,包括上Exhauster凸和下Exhauster凸,并利用函数的这种广义凸性,对无约束非光滑极小值和极大值问题,证明了在上Exhauster凸和下Exhauster凸性条件下最优性必要条件的充分性.A new class of generalized convex functions were defined by using differential Exhausters,including upper Exhauster convex function and lower Exhauster convex function.By using the generalized convexity of functions,we proved the sufficiency of the necessary conditions of optimality under the condition of upper Exhauster convexity and lower Exhauster convexity for unconstrained nonsmooth minimum and maximum problems.

关 键 词：Exhausters凸函数 广义凸函数 最优性条件 

分 类 号：O224[理学—运筹学与控制论]