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A doubly inexact proximal bundle method for convex optimization

Kouhei Harada (harada***at***msi.co.jp)

Abstract: We propose an extension of proximal bundle methods for minimizing a non-smooth convex function. Proximal bundle methods with inexact model minimization has been studied only under the assumption that oracles are exact and the stabilizing term is Bregman distance. We extends their results to let inexact model minimization compatible with inexact oracles and more generalized stabilizing term in the sense that the extended bundle method globally converges to an optimal point. Our extension of stabilizing term is new and it subsumes interior proximal distance. Our numerical experiments confirmed that allowing inexact model minimization often makes the proximal bundle method faster than its exact counterpart.

Keywords: bundle method, inexact oracle, proximal point, proximal distance

Category 1: Convex and Nonsmooth Optimization

Citation: Technical Report

Download: [PDF]

Entry Submitted: 04/13/2017
Entry Accepted: 04/13/2017
Entry Last Modified: 07/25/2018

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