A Conditional Gradient-Based Augmented Lagrangian Framework

This paper considers a generic convex minimization template with affine constraints over a compact domain, which covers key semidefinite programming applications. The existing conditional gradient methods either do not apply to our template or are too slow in practice. To this end, we propose a new conditional gradient method, based on a unified treatment of smoothing and augmented Lagrangian frameworks. The proposed method maintains favorable properties of the classical conditional gradient method, such as cheap linear minimization oracle calls and sparse representation of the decision variable. We prove O(1/√k) convergence rate of our method in the objective residual and the feasibility gap. This rate is essentially the same as the state of the art CG-type methods for our problem template, but the proposed method is significantly superior to existing methods in various semidefinite programming applications.

Published in:
Proceedings of the International Conference on Machine Learning - ICML 2019
Presented at:
36th International Conference on Machine Learning (ICML 2019), Long Beach, USA, June 9-15, 2019
Scheduled publication of Proceedings: Volume 97 is assigned to ICML 2019 (ISSN: 2640-3498)

Note: The status of this file is: Anyone

 Record created 2019-05-07, last modified 2020-04-20

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