非光滑悲观半向量双层规划的变分分析（英文）  

Variational analysis for pessimistic semivectorial bilevel programming with nonsmooth data

作　　者：刘兵兵 陈素根[1] LIU Bingbing;CHEN Sugen(School of Mathematics and Computational Science,Anqing Normal University,Anqing 246133,China;School of Management,University of Science and Technology of China,Hefei 230026,China)

机构地区：[1]安庆师范大学数学与计算科学学院,安徽安庆246133 [2]中国科学技术大学管理学院,安徽合肥230026

出　　处：《中国科学技术大学学报》2019年第5期351-367,共17页JUSTC

基　　金：Supported by the National Natural Science Foundation of China(61702012);the Scientific Research Foundation of the Higher Education Institutions of Anhui Province of China(KJ2017A361);the University Outstanding Young Talent Support Project of Anhui Province of China(gxyq2017026)

摘　　要：利用最近由Mordukhovich发展的变分分析理论,研究了悲观半向量双层规划问题,得到了在非光滑情形下的悲观半向量双层规划问题的必要最优性条件.为了得到该最优性条件,首先借助于标量化方法将悲观半向量双层规划问题转化为一个标量的双层优化问题.进而利用单层和两层值函数构造和Mordukhkvich广义微分计算规则,研究得到了所得的标量双层优化问题的一阶必要最优性条件,进而根据原悲观半向量双层规划问题与所得的标量双层优化问题的等价命题得到了原问题在非光滑情形下的一阶必要最优性条件.Using variational analysis theory developed recently by Mordukhovich,the pessimistic semivectorial bilevel programming problem(PSBPP) was investigated.PSBPP was first transformed into a scalar bilevel optimization problem with the help of a scalarization method.Furthermore,using single-level and two-level optimal value functions reformulations and generalized differentiation calculus of Mordukhovich,the first-order necessary optimality conditions were established for the resulting scalar bilevel optimization problem and thus for the PSBPP with nonsmooth data.

关 键 词：悲观半向量双层规划问题 必要最优性条件 李普希兹连续 最优值函数构造 灵敏度分析 

分 类 号：O221[理学—运筹学与控制论] O224[理学—数学]