Journal
MATHEMATICAL PROGRAMMING
Volume 155, Issue 1-2, Pages 199-230Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s10107-014-0841-6
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Funding
- AFOSR [FA9550-11-1-0141]
- MIT-Chile-Pontificia Universidad Catolica de Chile Seed Fund
- NSF Graduate Research Fellowship [1122374]
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We present new results for the Frank-Wolfe method (also known as the conditional gradient 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 FW gaps. Lastly, we present complexity bounds in the presence of approximate computation of gradients and/or linear optimization subproblem solutions.
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