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- W2116534411 abstract "We propose a primal-dual algorithmic framework for a prototypical constrained convex minimization problem. The new framework aims to trade-off the computational difficulty between the primal and the dual subproblems. We achieve this in our setting by replacing the standard proximal mapping computations with linear minimization oracles in the primal space, which has been the hallmark of the scalable Frank-Wolfe-type algorithms. Our analysis extends Nesterov's universal gradient methods to the primal-dual setting in a nontrivial fashion, and provides optimal convergence guarantees for the objective residual as well as the feasibility gap without having to know the smoothness structures of the problem. As a result, we obtain stronger primal-dual convergence results than the existing Frank-Wolfe-type algorithms for important machine learning problems involving sparsity and low-rank, and also illustrate them numerically." @default.
- W2116534411 created "2016-06-24" @default.
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- W2116534411 date "2015-02-10" @default.
- W2116534411 modified "2023-10-16" @default.
- W2116534411 title "Universal Primal-Dual Proximal-Gradient Methods" @default.
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