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

TL;DR

This paper introduces a parameter-free adaptive proximal bundle method for hybrid convex composite optimization that automatically adjusts stepsizes and improves computational efficiency and robustness over traditional methods.

Contribution

It proposes a novel parameter-free adaptive proximal bundle method with dynamic stepsize selection and criteria, enhancing efficiency and robustness in hybrid convex composite optimization.

Findings

Fewer null steps compared to traditional methods.

Significantly fewer total iterations needed.

Robust performance regardless of initial stepsize.

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.