Parameter-free proximal bundle methods with adaptive stepsizes for hybrid convex composite optimization problems

2024/10/28 by Renato D. C. Monteiro, Honghao Zhang, Monteiro, Renato D. C. +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #Aerospace Engineering and Control Systems #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2410.20751

openalex publication_date 2024/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

This paper develops a parameter-free adaptive proximal bundle method with two important features: 1) adaptive choice of variable prox stepsizes that "closely fits" the instance under consideration; and 2) adaptive criterion for making the occurrence of serious steps easier. Computational experiments show that our method performs substantially fewer consecutive null steps (i.e., a shorter cycle) while maintaining the number of serious steps under control. As a result, our method performs significantly less number of iterations than its counterparts based on a constant prox stepsize choice and a non-adaptive cycle termination criterion. Moreover, our method is very robust relative to the user-provided initial stepsize.

Cited by

• Heuristic Bundle Upper Bound Based Polyhedral Bundle Method for Semidefinite Programming

Related

• A unified analysis of a class of proximal bundle methods for solving hybrid convex composite optimization problems
• A proximal bundle variant with optimal iteration-complexity for a large range of prox stepsizes
• Proximal bundle methods for hybrid weakly convex composite optimization problems
• Universal subgradient and proximal bundle methods for convex and strongly convex hybrid composite optimization
• Optimal Convergence Rates for the Proximal Bundle Method