题     目：Zero-norm regularized problems: equivalent surrogates, proximal MM method and statistical error bound 

报 告 人：潘少华 教授

单     位：华南理工大学

时     间：2022年11月9日9：00

地     点：腾讯390-850-080

摘 要：For the zero-norm regularized problem, we verify that the penalty problem of its equivalent MPEC reformulation is a global exact penalty, which implies a family of equivalent surrogates. For a subfamily of these surrogates, the critical point set is demonstrated to coincide with the d-directional stationary point set and when a critical point has no too small nonzero component, it is a strongly local optimal solution of the surrogate problem and the zero-norm regularized problem. We also develop a proximal majorization-minimization (MM) method for solving the DC surrogates, and provide its global and linear convergence analysis. For the limit of the generated sequence, the statistical error bound is established under a mild condition, which implies its good quality from a statistical respective. Numerical comparisons with ADMM for solving the DC surrogate and APG for solving its partially smoothed form indicate that our proximal MM method armed with an inexact dual PPA plus the semismooth Newton method (PMMSN for short) is remarkably superior to ADMM and APG in terms of the quality of solutions and the CPU 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：锥约束优化及互补问题、低秩稀疏优化、结构非凸非光滑优化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；在国内外重要刊物如 Mathematical Programming, SIAM Journal on Optimization, SIAM Journal on Control and Optimization, Computational Optimization and Applications 等杂志发表论文50余篇。2019年荣获广东省自然科学奖二等奖。