A Unified Analysis of a Class of Proximal Bundle Methods for Solving Hybrid Convex Composite Optimization Problems
本文提出了一个基于通用束更新方案的近端束框架，用于求解混合凸复合优化问题，并统一建立了其迭代复杂度界，首次在混合凸复合优化背景下得到了三种变体的复杂度界。
This paper presents a proximal bundle (PB) framework based on a generic bundle 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 manner. 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. Funding: Financial support from the Office of Naval Research [N00014-18-1-2077] and the Air Force Office of Scientific Research [Grant FA9550-22-1-0088] is gratefully acknowledged.