求解双层凸优化问题的Forward-Backward分裂算法及其应用  

On the Forward-Backward Splitting Method for Solving Convex Bilevel Optimization Problems and Its Applications

作　　者：唐玥[1] 郭科[1] 赵世莲[1] TANG Yue;GUO Ke;ZHAO Shilian(College of Mathematics and Information,China West Normal University,Nanchong Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2018年第1期74-77,共4页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金(11371015);四川省高校创新团队(16TD0019);西华师范大学英才基金(17YC379)

摘　　要：Forward-Backward分裂算法是求解凸优化问题中的一个重要方法,本文考虑利用Forward-Backward分裂算法来求解双层凸优化问题,在一定的条件下,我们证明了算法的收敛性。由于变分不等式可以写成两个算子和的包含问题,因此作为应用,我们将得到的算法应用于研究变分不等式约束的双层优化问题,给出了其收敛性。文中所得到的结果,推广了Sabach和Shimrit等人的结果。The Forward-Backward splitting algorithm is an important method for solving the convex optimization problem.This paper discusses about the Forward-Backward splitting algorithm for solving bilevel optimization problem.The strong convergence of this algorithm under some suitable conditions is proved.As the variational inequality can be written as the sum of two operators inclusion,so the algorithm,as an application,is applied to study the bilevel optimization problem with the constraint of variational inequality and its convergence is also presented.The results obtained help to improve and extend the research of Sabach and Shimrit.

关 键 词：单调包含 极大单调算子 双层优化 凸极小化 分裂算法 变分不等式 

分 类 号：O221[理学—运筹学与控制论]