Applying FISTA to optimization problems (with or) without minimizers

• 成果类型: Article
• 署名作者: Bauschke, Heinz H.; Bui, Minh N.; Wang, Xianfu
• 署名单位: University of British Columbia; North Carolina State University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-019-01415-x
• 发表日期: 2020
• 页码: 349-381
• 关键词: convergence; algorithm

摘要

Beck and Teboulle's FISTA method for finding a minimizer of the sum of two convex functions, one of which has a Lipschitz continuous gradient whereas the other may be nonsmooth, is arguably the most important optimization algorithm of the past decade. While research activity on FISTA has exploded ever since, the mathematically challenging case when the original optimization problem has no minimizer has found only limited attention. In this work, we systematically study FISTA and its variants. We present general results that are applicable, regardless of the existence of minimizers.