New analysis and results for the Frank–Wolfe method
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10107_2014_841_ReferencePDF.pdf
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Author(s)
Freund, Robert Michael
Grigas, Paul Edward
Date Issued
November 2014
Journal
Mathematical Programming
Publisher
Springer Berlin Heidelberg
Citation
Freund, Robert M., and Paul Grigas. “New Analysis and Results for the Frank–Wolfe Method.” Math. Program. 155, no. 1–2 (November 28, 2014): 199–230.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
http://dx.doi.org/10.1007/s10107-014-0841-6
