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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Jiaming Liang & Renato D. C. Monteiro, 2024. "A Unified Analysis of a Class of Proximal Bundle Methods for Solving Hybrid Convex Composite Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 49(2), pages 832-855, May.
    • Handle: RePEc:inm:ormoor:v:49:y:2024:i:2:p:832-855
    DOI: 10.1287/moor.2023.1372
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    References listed on IDEAS

    as
    1. K. C. Kiwiel, 2000. "Efficiency of Proximal Bundle Methods," Journal of Optimization Theory and Applications, Springer, vol. 104(3), pages 589-603, March.
    2. Lemaréchal, C. & Nemirovskii, A. & Nesterov, Y., 1995. "New variants of bundle methods," LIDAM Reprints CORE 1166, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. NESTEROV, Yurii, 2015. "Universal gradient methods for convex optimization problems," LIDAM Reprints CORE 2701, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Vincent Guigues & Jiaming Liang & Renato D. C. Monteiro, 2026. "Universal Subgradient and Proximal Bundle Methods for Convex and Strongly Convex Hybrid Composite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 208(3), pages 1-33, March.

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