Corpus ID: 14121549

Convergence Rate of Frank-Wolfe for Non-Convex Objectives

@article{LacosteJulien2016ConvergenceRO,
  title={Convergence Rate of Frank-Wolfe for Non-Convex Objectives},
  author={S. Lacoste-Julien},
  journal={ArXiv},
  year={2016},
  volume={abs/1607.00345}
}
  • S. Lacoste-Julien
  • Published 2016
  • Mathematics, Computer Science
  • ArXiv
  • 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. Our analysis is affine invariant and is the first, to the best of our knowledge, giving a similar rate to what was already proven for projected gradient methods (though on slightly different measures of stationarity). 
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    References

    SHOWING 1-10 OF 16 REFERENCES
    On the Global Linear Convergence of Frank-Wolfe Optimization Variants
    • 233
    • PDF
    Revisiting Frank-Wolfe: Projection-Free Sparse Convex Optimization
    • M. Jaggi
    • Mathematics, Computer Science
    • ICML
    • 2013
    • 772
    • Highly Influential
    • PDF
    Accelerated gradient methods for nonconvex nonlinear and stochastic programming
    • 336
    • PDF
    The Complexity of Large-scale Convex Programming under a Linear Optimization Oracle
    • 88
    • PDF
    On the Complexity of Steepest Descent, Newton's and Regularized Newton's Methods for Nonconvex Unconstrained Optimization Problems
    • 164
    • Highly Influential
    • PDF
    Mini-batch stochastic approximation methods for nonconvex stochastic composite optimization
    • 216
    • Highly Influential
    • PDF
    Global Convergence of a Class of Trust Region Algorithms for Optimization Using Inexact Projections on Convex Constraints
    • 60
    • PDF
    Introductory Lectures on Convex Optimization - A Basic Course
    • 4,018
    • Highly Influential