An Inexact Bregman Proximal Difference-of-Convex Algorithm with Two Types of Relative Stopping Criteria

报告摘要：In this talk, we consider a class of difference-of-convex (DC) optimization problems, where the global Lipschitz gradient continuity assumption on the smooth part of the objective function is not required. Such problems are prevalent in many contemporary applications such as compressed sensing, statistical regression, and machine learning, and can be solved by a general Bregman proximal DC algorithm (BPDCA). However, the existing BPDCA is developed based on the stringent requirement that the involved subproblems must be solved exactly, which is often impractical and limits the applicability of the BPDCA. To facilitate the practical implementations and wider applications of the BPDCA, we develop an inexact Bregman proximal difference-of-convex algorithm (iBPDCA) by incorporating two types of relative-type stopping criteria for solving the subproblems. The proposed inexact framework has considerable flexibility to encompass many existing exact and inexact methods, and can accommodate different types of errors that may occur when solving the subproblem. This enables the potential application of our inexact framework across different DC decompositions to facilitate the design of a more efficient DCA scheme in practice. The global subsequential convergence and the global sequential convergence of our iBPDCA are established under suitable conditions including the Kurdyka-Lojasiewicz property. Some numerical experiments on the l1-l2 regularized least squares problem and the constrained l1-l2 sparse optimization problem are conducted to show the superior performance of our iBPDCA in comparison to existing algorithms. These results also empirically verify the necessity of developing different types of stopping criteria to facilitate the efficient computation of the subproblem in each iteration of our iBPDCA.

报告人简介：杨磊，中山大学计算机学院“百人计划”副教授，广东省计算科学重点实验室成员。本硕毕业于天津大学，博士毕业于香港理工大学，博士毕业后先后在新加坡国立大学和香港理工大学从事博士后研究工作。主要从事最优化理论和算法研究，特别专注于为机器学习和图像处理等应用领域中出现的大规模优化问题设计和分析高效稳健的优化算法，以及相关求解器的开发。目前已在SIOPT, MOR, JSC, JMLR, SIIMS, TSP等国际重要期刊上发表多篇论文；博士学位论文荣获《香港数学会最佳博士学位论文奖》；荣获教育部第一批海外博士后引才专项；主持国家级、省部级以及市级等各级项目多项；担任中国运筹学会数学规划分会青年理事。