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arXiv · 1605.02970

Fast Primal-Dual Gradient Method for Strongly Convex Minimization Problems with Linear Constraints

Alexey Chernov·Pavel Dvurechensky·Alexander Gasnikov
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Abstract

In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality constraints. A number of optimization problems in applications can be stated in this form, examples being the entropy-linear programming, the ridge regression, the elastic net, the regularized optimal transport, etc. We extend the Fast Gradient Method applied to the dual problem in order to make it primal-dual so that it allows not only to solve the dual problem, but also to construct nearly optimal and nearly feasible solution of the primal problem. We also prove a theorem about the convergence rate for the proposed algorithm in terms of the objective function and the linear constraints infeasibility.

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Alexey Chernov, Pavel Dvurechensky, Alexander Gasnikov. 2016-05-10. Fast Primal-Dual Gradient Method for Strongly Convex Minimization Problems with Linear Constraints. https://arxiv.org/abs/1605.02970

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