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An Extended Frank-Wolfe Method with “In-Face” Directions, and its Application to Low-Rank Matrix Completion

Robert M. Freund(rfreund***at***mit.edu)
Paul Grigas(pgrigas***at***mit.edu)
Rahul Mazumder(rahulmaz***at***mit.edu)

Abstract: We present an extension of the Frank-Wolfe method that is designed to induce near-optimal solutions on low-dimensional faces of the feasible region. We present computational guarantees for the method that trade off efficiency in computing near-optimal solutions with upper bounds on the dimension of minimal faces of iterates. We apply our method to the low-rank matrix completion problem, where low-dimensional faces correspond to low-rank solutions. We present computational results for large-scale low-rank matrix completion problems that demonstrate significant speed-ups in computing low-rank near-optimal solutions on both artificial and real datasets.

Keywords: matrix completion, Frank-Wolfe, conditional gradient, low-rank, nuclear norm, first-order methods

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Applications -- Science and Engineering (Data-Mining )

Citation: MIT Operations Research Center Working Paper, November, 2015

Download: [PDF]

Entry Submitted: 11/06/2015
Entry Accepted: 11/06/2015
Entry Last Modified: 11/06/2015

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