A proximal method for composite minimization

• 成果类型: Article
• 署名作者: Lewis, A. S.; Wright, S. J.
• 署名单位: Cornell University; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-015-0943-9
• 发表日期: 2016
• 页码: 501-546
• 关键词: point algorithm; active constraints; variable selection; optimization; CONVERGENCE; identification; shrinkage; systems

摘要

We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe an algorithmic framework based on a subproblem constructed from a linearized approximation to the objective and a regularization term. Properties of local solutions of this subproblem underlie both a global convergence result and an identification property of the active manifold containing the solution of the original problem. Preliminary computational results on both convex and nonconvex examples are promising.