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

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