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Adaptive Linearized Alternating Direction Method of Multipliers for Non-Convex Compositely Regularized Optimization Problems

查看全文 作　　者：Linbo [1]Qiao;Bofeng [2]Zhang;Xicheng [1]Lu;Jinshu [1]Su 高影响力作者 机构地区：[1]College of Computer,National University of Defense Technology,and National Laboratory for Parallel and Distributed Processing,National University of Defense Technology,Changsha 410073,China;[2]College of Computer,National University of Defense Technology,Changsha 410073,China高影响力机构 出　　处：《Tsinghua Science and Technology》索引2017年第22卷第3期,共14页高影响力期刊 基　　金：supported by the National Natural Science Foundation of China(Nos.61303264,61202482,and 61202488);Guangxi Cooperative Innovation Center of Cloud Computing and Big Data(No.YD16505);Distinguished Young Scientist Promotion of National University of Defense Technology 摘　　要：We consider a wide range of non-convex regularized minimization problems, where the non-convex regularization term is composite with a linear function engaged in sparse learning. Recent theoretical investigations have demonstrated their superiority over their convex counterparts. The computational challenge lies in the fact that the proximal mapping associated with non-convex regularization is not easily obtained due to the imposed linear composition. Fortunately, the problem structure allows one to introduce an auxiliary variable and reformulate it as an optimization problem with linear constraints, which can be solved using the Linearized Alternating Direction Method of Multipliers(LADMM). Despite the success of LADMM in practice, it remains unknown whether LADMM is convergent in solving such non-convex compositely regularized optimizations. In this research, we first present a detailed convergence analysis of the LADMM algorithm for solving a non-convex compositely regularized optimization problem with a large class of non-convex penalties. Furthermore, we propose an Adaptive LADMM(Ada LADMM) algorithm with a line-search criterion. Experimental results on different genres of datasets validate the efficacy of the proposed algorithm. 关 键 词：凸优化问题 线性函数 交替方向 复合化 乘子法 自适应 线性约束优化问题 非凸优化
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