Composite proximal bundle method

• 成果类型: Article
• 署名作者: Sagastizabal, Claudia
• 署名单位: Instituto Nacional de Matematica Pura e Aplicada (IMPA)
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-012-0600-5
• 发表日期: 2013
• 页码: 189-233
• 关键词: gauss-newton method; convex-functions; CONVERGENCE; algorithms; smooth

摘要

We consider minimization of nonsmooth functions which can be represented as the composition of a positively homogeneous convex function and a smooth mapping. This is a sufficiently rich class that includes max-functions, largest eigenvalue functions, and norm-1 regularized functions. The bundle method uses an oracle that is able to compute separately the function and subgradient information for the convex function, and the function and derivatives for the smooth mapping. With this information, it is possible to solve approximately certain proximal linearized subproblems in which the smooth mapping is replaced by its Taylor-series linearization around the current serious step. Our numerical results show the good performance of the Composite Bundle method for a large class of problems.