A Conditional Gradient Framework for Composite Convex Minimization with Applications to Semidefinite Programming

Abstract :

We propose a conditional gradient framework for a composite convex minimization template with broad applications. Our approach combines the notions of smoothing and homotopy under the CGM framework, and provably achieves the optimal O(1/√k) convergence rate. We demonstrate that the same rate holds if the linear subproblems are solved approximately with additive or multiplicative error. Specific applications of the framework include the non-smooth minimization, semidefinite programming, and minimization with linear inclusion constraints over a compact domain. We provide numerical evidence to demonstrate the benefits of the new framework.

Document type :
Conference papers
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https://hal.telecom-paristech.fr/hal-02292460
Contributor : Telecomparis Hal <>
Submitted on : Thursday, September 19, 2019 - 7:25:27 PM
Last modification on : Saturday, September 21, 2019 - 1:16:22 AM

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  • HAL Id : hal-02292460, version 1

Citation

Alp Yurtsever, Olivier Fercoq, Volkan Cevher, Francesco Locatello. A Conditional Gradient Framework for Composite Convex Minimization with Applications to Semidefinite Programming. International Conference on Machine Learning, Jul 2018, Stockholm, Sweden. ⟨hal-02292460⟩

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