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Level-set methods for convex optimization

Aleksandr Y. Aravkin(saravkin***at***uw.edu )
James V. Burke(jvburke***at***uw.edu )
Dmitriy Drusvyatskiy(ddrusv***at***uw.edu)
Michael P. Friedlander(mpf***at***math.ucdavis.edu )
Scott Roy(scottroy***at***uw.edu)

Abstract: Convex optimization problems arising in applications often have favorable objective functions and complicated constraints, thereby precluding first-order methods from being immediately applicable. We describe an approach that exchanges the roles of the objective and constraint functions, and instead approximately solves a sequence of parametric level-set problems. A zero-finding procedure, based on inexact function evaluations and possibly inexact derivative information, leads to an efficient solution scheme for the original problem. We describe the theoretical and practical properties of this approach for a broad range of problems, including low-rank semidefinite optimization, sparse optimization, and generalized linear models for inference.

Keywords: level-sets, root finding, Newton and secant methods, gauges, sparse and low-rank recovery

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation:

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Entry Submitted: 02/23/2016
Entry Accepted: 02/23/2016
Entry Last Modified: 02/23/2016

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