报告题目：A Hybrid First-order Method for NonconvexLp-ball Constrained Optimization

报告人：王浩助理教授 上海科技大学

邀请人：赵志华何超讲师

报告时间：2022年4月14日（周四）14:00-16:00

腾讯会议ID：646-573-527

报告人简介：王浩博士，上海市青年东方学者。现任上海科技大学信息科学与技术学院助理教授，于2015年5月在美国Lehigh大学工业工程系获得博士学位，并于2010年和2007年在北京航空航天大学数学与应用数学系分别获得理学硕士和学士学位。曾分别在埃克森美孚企业战略实验室、三菱电机研究实验室和群邑集团研发部担任实习研究员。当前研究领域主要为惩罚算法、非精确算法、非凸正则化问题等机器学习问题和算法。主要成果在SIAM Journal on Optimization、Computational Optimization and Applications、Journal of Optimization Theory and Applications、Optimization Methods and Software等刊物上发表。主持国家自然科学基金项目1项，上海市自然科学基金项目1项。

报告摘要：In this talk, we consider the nonconvex optimization problem in which the objective is continuously differentiable and the feasible set is a nonconvex lp ball. Studying such optimization offers the possibility to bridge the gap between a range of intermediate values 0<p<1 and p=0,1 in the norm-constraint sparse optimization, both in theory and practice. We propose a novel hybrid method within a first-order algorithmic framework for solving such problems by combining the Frank-Wolfe method and the gradient projection method. During iteration, it solves a Frank-Wolfe subproblem if the current iterate is in the interior of the lp ball, and it solves a gradient projection subproblem with a weighted l1-ball constraint if the current iterate is on the boundary of the lp ball. Global convergence is proved, and a worst-case ergodic O(1/k) convergence rate of the optimality error is also established for convex objectives. We believe that the proposed method is the first practical algorithm for solving lp-ball constrained nonlinear problems with theoretical guarantees. Numerical experiments demonstrate the practicability and efficiency of the proposed algorithm.