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A doubly inexact interior proximal bundle method for convex optimization

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

Abstract: We propose a version of bundle method for minimizing a non-smooth convex function. Our bundle method have three features. In bundle method, we approximate the objective with some cutting planes and minimize the model with some stabilizing term. Firstly, it allows inexactness in this minimization. At the same time, evaluations of the objective and the subgradient are also required to generate the cutting planes. Secondly, inexact evaluation is also allowed. In this sense, our algorithm is doubly inexact. Thirdly, the stabilizing term are not assumed to be quadratic. We use interior proximal distance which was developed by Auslender and Teboulle, as the stabilizing term. We show that it globally converges to an optimal solution. Furthermore, it is also applicable to Lagrange relaxation problems. We show that both primal feasibility and optimality are asymptotically achieved.

Keywords: bundle method, Lagrangian relaxation, inexact oracle, primal recovery, 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: 01/07/2018

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