BUNDLE METHODS IN THE XXIst CENTURY: A BIRD'S-EYE VIEW

Abstract

Bundle methods are often the algorithms of choice for nonsmooth convex optimization, especially if accuracy in the solution and reliability are a concern. We review several algorithms based on the bundle methodology that have been developed recently and that, unlike their forerunner variants, have the ability to provide exact solutions even if most of the time the available information is inaccurate. We adopt an approach that is by no means exhaustive, but covers different proximal and level bundle methods dealing with inexact oracles, for both unconstrained and constrained problems.