求解双层凸优化问题的Forward-Backward分裂算法  

Forward-Backward Splitting Method for Solving Convex Bilevel Optimization Problems

作　　者：李明川 叶明露[1] LI Mingchuan;YE Minglu(School 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）》2020年第1期46-51,共6页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(11871059,11801455)。

摘　　要：Forward-Backward分裂算法是求解极大单调算子和问题以及极小化具有可分结构的凸函数和问题的有效算法。本文利用该算法在Hilbert空间中构造出了求解双层优化问题的分裂算法。与已有文献相比,所提算法不仅在参数的选取上更加灵活,而且本文还证明了该算法生成的点列能收敛到双层优化问题的解。Forward-Backward splitting algorithm is an efficient method for solving the sum of maximal monotone mappings and minimizing the sum of convex functions with splitting construct.Taking advantage of the algorithm,a method is generalized in Hilbert space for solving bilevel optimization problems in this paper.The parameters of the algorithm is more flexible when compared with the known methods.It is also proved that points sequence generated by the algorithm can converge to the solution of bilevel optimization problems.

关 键 词：极大单调算子 双层优化 非扩张映射 Forward-Backward算法 弱收敛列 

分 类 号：O221[理学—运筹学与控制论]