报告人：沈春根 教授（上海理工大学）
时间：2022年10月13日，10:30-11:30
腾讯会议 ID：164-528-190
摘要：
In this talk, we introduce an active-set proximal-Newton algorithm for solving $\ell_1$ regularized convex/nonconvex optimization problems subject to box constraints. Our algorithm first relies on the KKT error to estimate the active and free variables, and then smoothly combines the proximal gradient iteration and the Newton iteration to efficiently pursue the convergence of the active and free variables, respectively. The global convergence is analyzed without assuming the convexity of the objective function. We also establish the fast local convergence of the active-set proximal-Newton algorithm under the second-order sufficient condition and some strict-complementarity-like conditions. For some structured convex problems, we further design a safe screening procedure that is able to identify/remove active variables, and can be integrated into the basic active-set proximal-Newton algorithm to accelerate the convergence. The algorithm is evaluated on various synthetic and real data, and the efficiency is demonstrated particularly on $\ell_1$ regularized convex/nonconvex quadratic programs and logistic regression problems.
邀请人：张雷洪