报告时间：2020年12月12日上午9:30

报告地点：腾讯会议（会议 ID：501 778 113）

线下地点：工西416

报告摘要：This paper is concerned with a class of zero-norm regularized piecewise linear-quadratic (PLQ) composite optimization problems, which covers the zero-norm regularized $\ell_1$-loss minimization problem as a special case.  For this class of nonconvex nonsmooth and non-Lipschitz optimization problems, we show that its equivalent MPEC reformulation is partially calm on the set of global optima and make use of this property to derive a family of equivalent DC surrogates. Then, we propose a proximal majorization-minimization (MM) method, a convex relaxation approach different from the DC algorithms, for solving one of the DC surrogates, a two-block nonsmooth semiconvex PLQ optimization problem. For this method, we establish its global convergence and linear rate of convergence and show that under mild conditions the limit of the generated sequence is not only a local minimum but also a good critical point in a statistical sense. Numerical experiments are conducted with synthetic and real data for the proximal MM method with the subproblems solved by a dual semismooth Newton method to confirm our theoretical findings, and numerical comparisons with a convergent indefinite-proximal ADMM for the partially smoothed DC surrogate verify its superiority in the quality of solutions and computing time.

报告人简介：潘少华，华南理工大学数学学院教授、博士生导师。现任中国运筹学会理事和中国运筹学会数学规划分会常务理事。研究方向：低秩稀疏优化问题、锥约束优化与互补问题的理论与算法研究。主持国家自科基金和广东省自科基金各2项。在国际重要优化刊物Mathematical Programming, SIAM Journal on Optimization, SIAM Journal on Control and Optimization, Computational Optimization and Applications 等杂志发表论文30余篇，2019年荣获广东省自然科学二等奖。