New analysis and results for the Frank–Wolfe method

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 ru...

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Bibliographic Details
Published in:Mathematical programming Vol. 155; no. 1-2; pp. 199 - 230
Main Authors: Freund, Robert M., Grigas, Paul
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2016
Springer Nature B.V
Subjects:
Accuracy
Approximation
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Computation
Constants
Convex analysis
Full Length Paper
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical models
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Methods
Numerical Analysis
Optimization
Scholarships & fellowships
Sequences
Sparsity
Studies
Theoretical
90C06
90C25
65K05
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary: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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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-014-0841-6