Path-Following Gradient-Based Decomposition Algorithms For Separable Convex Optimization

Details Path-Following Gradient-Based Decomposition Algorithms For Separable Convex Optimization Path-Following Gradient-Based Decomposition Algorithms For Separable Convex Optimization

2012-03-16

arxiv.org/abs/1203.3742v1

Mathematics

Optimization and Control

8 pages, 1 figure, 1 table. Submitted to 2012 IEEE Conference on Decision and Control

Scientific paper

A new distributed optimization algorithm, called path-following gradient-based decomposition, is proposed to solve separable convex optimization problems. This algorithm is a combination of three techniques: smoothing, Lagrangian decomposition and path-following gradient method. By applying a smoothing technique via barrier functions, we show that the dual problem possesses smoothness properties which make it suitable for applying a first order method of multiplier and lead to a decomposition scheme. We prove the global convergence of the algorithm and analyze its local convergence rate. Then, we modify the proposed algorithm by applying Nesterov's accelerating scheme to get a new variant which has a better local convergence rate. Finally, we present preliminary numerical tests that confirm the theory development.

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