Composite Proximal Bundle Method

Claudia Sagastizabal (sagastizimpa.br)

Abstract: We consider minimization of nonsmooth functions which can be represented as the composition of a positively homogeneous convex function and a smooth mapping. This is a sufficiently rich class that includes max-functions, largest eigenvalue functions, and norm-1 regularized functions. The bundle method uses an oracle that is able to compute separately the function and subgradient information for the convex function, and the function and derivatives for the smooth mapping. With this information, it is possible to solve approximately certain proximal linearized subproblems in which the smooth mapping is replaced by its Taylor-series linearization around the current serious step. Our numerical results show the good performance of the Composite Bundle method for a large class of problems.

Keywords: nonsmooth optimization, bundle methods, composite functions

Category 1: Convex and Nonsmooth Optimization

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

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Entry Submitted: 07/30/2009
Entry Accepted: 07/30/2009
Entry Last Modified: 04/27/2011

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