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.
作者
刘兵兵
陈素根
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)
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)
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
pessimistic semivectorial bilevel programming problem
necessary optimality condition
Lipschitz continuous
optimal value function reformulation
sensitivity analysis
