Linearized Proximal Algorithms for Convex Composite Optimization with Applications

Time: 2021-11-16 10:27:00

Topic： Linearized Proximal Algorithms for Convex Composite Optimization with Applications

Speaker：Yaohua Hu   Shenzhen University

Time：2021-11-15  16:00--17:00

Location：Room401

Introduction：

    In this talk, we consider the convex composite optimization (CCO) problem that provides a unified framework of a wide variety of important optimization problems, such as convex inclusions, penalty methods for nonlinear programming, and regularized minimization problems. We will introduce a linearized proximal algorithm (LPA) to solve the CCO. The LPA has the attractive computational advantages of simple implementation and fast convergence rate. Under the assumptions of local weak sharp minima of Holderian order and a quasi-regularity condition, we establish a local/semi-local/global superlinear convergence rate for the LPA-type algorithms. We further apply the LPA to solve a (possibly nonconvex) feasibility problem, as well as a sensor network localization problem. Our numerical results illustrate that the LPA meets the demand for an efficient and robust algorithm for the sensor network localization problem.