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We give a simple proof that the Frank-Wolfe algorithm obtains a stationary point at a rate of $O(1/\sqrt{t})$ on non-convex objectives with a Lipschitz continuous gradient.
An algorithm for quadratic programming
M. Frank and P. Wolfe · 1956
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Approximate methods in optimization problems
V. F. Demyanov and A. M. Rubinov · 1970
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Rates of convergence for conditional gradient algorithms near singular and nonsingular extremals
J. C. Dunn · 1979
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Global convergence of a class of trust region algorithms for optimization using inexact projections on convex constraints
A. R. Conn, N. Gould, A. Sartenaer, and P. L. Toint · 1993
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Nonlinear programming
D. P. Bertsekas · 1999
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Introductory Lectures on Convex Optimization
Y. Nesterov · 2004
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On the complexity of steepest descent, Newton’s and regularized Newton’s methods for nonconvex unconstrained optimization problems
C. Cartis, N. I. M. Gould, and P. L. Toint · 2010
Cited alongside, same era.
An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity
C. Cartis, N. I. M. Gould, and P. L. Toint · 2012
Cited alongside, same era.
Revisiting Frank-Wolfe: Projection-free sparse convex optimization
M. Jaggi · 2013
Cited alongside, same era.
The complexity of large-scale convex programming under a linear optimization oracle
G. Lan · 2013
Cited alongside, same era.
Generalized conditional gradient for sparse estimation
Y. Yu, X. Zhang, and D. Schuurmans · 2014
Cited alongside, same era.
On pairwise costs for network flow multi-object tracking
V. Chari, S. Lacoste-Julien, I. Laptev, and J. Sivic · 2015
Later among the works it cites.
On the global linear convergence of Frank-Wolfe optimization variants
S. Lacoste-Julien and M. Jaggi · 2015
Later among the works it cites.
Unsupervised learning from narrated instruction videos
J.-B. Alayrac, P. Bojanowski, N. Agrawal, I. Laptev, J. Sivic, and S. Lacoste-Julien · 2016
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Accelerated gradient methods for nonconvex nonlinear and stochastic programming
S. Ghadimi and G. Lan · 2016
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Mini-batch stochastic approximation methods for nonconvex stochastic composite optimization
S. Ghadimi, G. Lan, and H. Zhang · 2016
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