A bundle method using two polyhedral approximations of the epsilon-enlargement of a maximal monotone operator

TL;DR

This paper introduces a novel bundle method leveraging two polyhedral approximations of the epsilon-enlargement of a maximal monotone operator, aiming to efficiently find zeros of such operators.

Contribution

It presents a new algorithm that uses double polyhedral approximations and the transportation formula, potentially inspiring methods for split operators.

Findings

Algorithm effectively finds zeros of maximal monotone operators.

Double approximation approach offers new insights for bundle methods.

Potential applications in splitting methods for complex operators.

Abstract

In this work, we develop a variant of a bundle method in order to find a zero of a maximal monotone operator. This algorithm relies on two polyhedral approximations of the epsilon-enlargement of the considered operator, via a systematic use of the transportation formula. Moreover, the use of a double polyhedral approximation in our algorithm could inspire other bundle methods for the case where the given operator can be split as the sum of two other maximal monotone operators.