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Dynamical Primal-Dual Accelerated Method with Applications to Network Optimization
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abstract
This paper develops a continuous-time primal-dual accelerated method with an increasing damping coefficient for a class of convex optimization problems with affine equality constraints. This paper analyzes critical values for parameters in the proposed method and prove that the rate of convergence in terms of the duality gap function is $O(\tfrac{1}{t^2})$ by choosing suitable parameters. As far as we know, this is the first continuous-time primal-dual accelerated method that can obtain the optimal rate. Then this work applies the proposed method to two network optimization problems, a distributed optimization problem with consensus constraints and a distributed extended monotropic optimization problem, and obtains two variant distributed algorithms. Finally, numerical simulations are given to demonstrate the efficacy of the proposed method.
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Cited by 1 Pith paper
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Continuous and discrete-time accelerated methods for an inequality constrained convex optimization problem
A Bregman Lagrangian with a logarithmic barrier leads to a continuous-time dynamical system and discrete accelerated methods that converge to the solution of convex inequality-constrained problems.
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