讲座题目Alternating Direction Method of Multipliers with Adaptive Proximal Terms for Convex Optimization Problems


报告专家顾燕(南京航空航天大学 讲师)

报告时间20211125(周四) 10:00-11:00


专家简介顾燕,南京航空航天大学理学院讲师。2020年博士毕业于日本京都大学。主要研究兴趣为结构型优化的分裂算法的理论研究,以及交通优化、机器学习等方面的应用研究。在European Journal of Operational ResearchComputational and Applied Mathematics等期刊上发表文章5篇,论文被引47次。20181月到2月在美国罗格斯大学访问,20194月到20203月在京都大学人工智能专业担任特别研究员,20204月到202012月在京都大学数理工学专业担任共同研究员

摘要: The alternating direction method of multipliers (ADMM) is an effective method for solving wide fields of convex problems. At each iteration, the classical ADMM solves two subproblems exactly. However, in many applications, it is expensive or impossible to obtain the exact solutions of the subproblems. To overcome the difficulty, some proximal terms are added to the subproblems. We proposed a variable metric indefinite proximal ADMM, and give sufficient conditions on the proximal terms for the global convergence. Furthermore, based on the BFGS update (or limited memory BFGS), we propose a new semidefinite/indefinite proximal term which can satisfy the conditions for the global convergence. Experiments on several datasets demonstrated that our proposed algorithms outperform most of the comparison proximal ADMMs.