A proximal method for composite minimization

A.S. Lewis(aslewisorie.cornell.edu)
S.J. Wright(swrightcs.wisc.edu)

Abstract: We consider minimization of functions that are compositions of prox-regular functions with smooth vector functions. A wide variety of important optimization problems can be formulated in this way. We describe a subproblem constructed from a linearized approximation to the objective and a regularization term, investigating the properties of local solutions of this subproblem and showing that they eventually identify a manifold containing the solution of the original problem. We propose an algorithmic framework based on this subproblem and prove a global convergence result.

Keywords: prox-regular functions, polyhedral convex functions, sparse optimization, global convergence, active constraint identification

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: School of ORIE, Cornell University. Computer Sciences Department, University of Wisconsin.

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Entry Submitted: 12/01/2008
Entry Accepted: 12/01/2008
Entry Last Modified: 12/01/2008

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