Frank-Wolfe type methods for nonconvex inequality-constrained problems

发布时间：2022-11-30 作者：77779193永利官网浏览次数：

Speaker:	曾燎原	DateTime:	2022年12月7日（星期三）上午11：00--12：00
Brief Introduction to Speaker: 曾燎原，副研究员，浙江工业大学		Place:	腾讯会议（252676993）
Abstract:The Frank-Wolfe (FW) method, which implements efficient linear oracles that minimize linear approximations of the objective function over a fixed compact convex set, has recently received much attention in the optimization and machine learning literature. In this talk, I will introduce a new FW-type method for minimizing a smooth function over a compact set defined by a single nonconvex inequality constraint, based on new generalized linear-optimization oracles (LO). These LOs can be computed efficiently with closed-form solutions in some important optimization models that arise in compressed sensing and machine learning. Under a mild strict feasibility condition, the subsequential convergence of this nonconvex FW method can be established. In addition, I will introduce an away-step oracle that supplements our nonconvex FW method. Finally, numerical tests of the proposed FW method and its away-step variant on a matrix completion problem will be presented.