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Bundle methods in the XXIst century: A bird's-eye view

Welington de Oliveira(wlo***at***impa.br)
Claudia Sagastiz√°bal(sagastiz***at***impa.br)

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 di erent proximal and level bundle methods dealing with inexact oracles, for both unconstrained and constrained problems.

Keywords: bundle methods, inexact oracles, nonsmooth convex optimization

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )


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Entry Submitted: 10/21/2013
Entry Accepted: 10/21/2013
Entry Last Modified: 10/21/2013

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