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Primal-dual Accelerated Mirror-Descent Method for Constrained Bilinear Saddle-Point Problems
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abstract
We develop a first-order accelerated algorithm for a class of constrained bilinear saddle-point problems with applications to network systems. The algorithm is a modified time-varying primal-dual version of an accelerated mirror-descent dynamics. It deals with constraints such as simplices and convex set constraints effectively, and converges with a rate of $O(1/t^2)$. Furthermore, we employ the acceleration scheme to constrained distributed optimization and bilinear zero-sum games, and obtain two variants of distributed accelerated algorithms.
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Nesterov acceleration for strongly convex-strongly concave bilinear saddle point problems: discrete and continuous-time approaches
A Nesterov-accelerated primal-dual gradient algorithm and its continuous-time analogue achieve O((1 - min{sqrt(mu_F/L_F), sqrt(mu_G/L_G)})^k) convergence for strongly convex-strongly concave bilinear saddle point problems.
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