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 convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe an algorithmic framework based on a subproblem constructed from a linearized approximation to the objective and a regularization term. Properties of local solutions of this subproblem underlie both a global convergence result and an identification property of the active manifold containing the solution of the original problem. Preliminary computational results on both convex and nonconvex examples are promising.

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: 10/20/2014

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