A Unified Analysis of a Class of Proximal Bundle Methods for Solving Hybrid Convex Composite Optimization Problems br

• 成果类型: Article
• 署名作者: Liang, Jiaming; Monteiro, Renato D. C.
• 署名单位: Yale University; University System of Georgia; Georgia Institute of Technology
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• 发表日期: 2024
• 页码: 832-855
• 关键词: maximum

摘要

This paper presents a proximal bundle (PB) framework based on a generic bun-dle update scheme for solving the hybrid convex composite optimization (HCCO) problem and establishes a common iteration-complexity bound for any variant belonging to it. As a consequence, iteration-complexity bounds for three PB variants based on different bundle update schemes are obtained in the HCCO context for the first time and in a unified man-ner. Although two of the PB variants are universal (i.e., their implementations do not require parameters associated with the HCCO instance), the other newly (as far as the authors are aware) proposed one is not, but has the advantage that it generates simple- namely, one-cut-bundle models. The paper also presents a universal adaptive PB variant (which is not necessarily an instance of the framework) based on one-cut models and shows that its iteration-complexity is the same as the two aforementioned universal PB variants.