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New Analysis and Results for the Conditional Gradient Method

Robert Freund (rfreund***at***mit.edu)
Paul Grigas (pgrigas***at***mit.edu)

Abstract: We present new results for the conditional gradient method (also known as the Frank-Wolfe method). We derive computational guarantees for arbitrary step-size sequences, which are then applied to various step-size rules, including simple averaging and constant step-sizes. We also develop step-size rules and computational guarantees that depend naturally on the warm-start quality of the initial (and subsequent) iterates. Our results include computational guarantees for both duality/bound gaps and the so-called Wolfe gaps. Lastly, we present complexity bounds in the presence of approximate computation of gradients and/or linear optimization subproblem solutions.

Keywords: conditional gradient, Frank-Wolfe, computational complexity, warm start, inexact computation

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: MIT Operations Research Center Working Paper OR395-13, July 2013

Download: [PDF]

Entry Submitted: 07/01/2013
Entry Accepted: 07/01/2013
Entry Last Modified: 07/10/2013

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