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

Jiaming Liang () and Renato D. C. Monteiro ()
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Jiaming Liang: Department of Computer Science, Yale University, New Haven, Connecticut 06511
Renato D. C. Monteiro: School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332

Mathematics of Operations Research, 2024, vol. 49, issue 2, 832-855

Abstract: 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.

Keywords: 49M37; 65K05; 68Q25; 90C25; 90C30; 90C60; hybrid convex composite optimization; iteration-complexity; proximal bundle method; universal method (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:49:y:2024:i:2:p:832-855

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