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This paper presents a proximal bundle (PB) framework based on a genericbundle update scheme for solving the hybrid convex composite optimization(HCCO) problem and establishes a common iteration-complexity bound for anyvariant belonging to it. As a consequence, iteration-complexity bounds forthree PB variants based on different bundle update schemes are obtained in theHCCO context for the first time and in a unified manner. While two of the PBvariants are universal (i.e., their implementations do not require parametersassociated with the HCCO instance), the other newly (as far as the authors areaware of) proposed one is not but has the advantage that it generates simple,namely one-cut, bundle models. The paper also presents a universal adaptive PBvariant (which is not necessarily an instance of the framework) based onone-cut models and shows that its iteration-complexity is the same as the twoaforementioned universal PB variants.

A unified analysis of a class of proximal bundle methods for solving hybrid convex composite optimization problems