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arXiv · 1506.02530

Linear Convergence of the Randomized Feasible Descent Method Under the Weak Strong Convexity Assumption

Chenxin Ma·Rachael Tappenden·Martin Takáč
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Abstract

In this paper we generalize the framework of the feasible descent method (FDM) to a randomized (R-FDM) and a coordinate-wise random feasible descent method (RC-FDM) framework. We show that the famous SDCA algorithm for optimizing the SVM dual problem, or the stochastic coordinate descent method for the LASSO problem, fits into the framework of RC-FDM. We prove linear convergence for both R-FDM and RC-FDM under the weak strong convexity assumption. Moreover, we show that the duality gap converges linearly for RC-FDM, which implies that the duality gap also converges linearly for SDCA applied to the SVM dual problem.

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Chenxin Ma, Rachael Tappenden, Martin Takáč. 2015-06-08. Linear Convergence of the Randomized Feasible Descent Method Under the Weak Strong Convexity Assumption. https://arxiv.org/abs/1506.02530

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