Accelerated Dual Descent for Network Optimization
Author(s)Zargham, Michael; Ribeiro, Alejandro; Ozdaglar, Asuman E.; Jadbabaie, Ali
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Dual descent methods are commonly used to solve network optimization problems because their implementation can be distributed through the network. However, their convergence rates are typically very slow. This paper introduces a family of dual descent algorithms that use approximate Newton directions to accelerate the convergence rate of conventional dual descent. These approximate directions can be computed using local information exchanges thereby retaining the benefits of distributed implementations. The approximate Newton directions are obtained through matrix splitting techniques and sparse Taylor approximations of the inverse Hessian.We show that, similarly to conventional Newton methods, the proposed algorithm exhibits superlinear convergence within a neighborhood of the optimal value. Numerical analysis corroborates that convergence times are between one to two orders of magnitude faster than existing distributed optimization methods. A connection with recent developments that use consensus iterations to compute approximate Newton directions is also presented.
URL to paper listed on conference site
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Proceedings of American Control Conference (ACC 2011)
IEEE Control Systems Society
Zargham, Michael et al."Accelerated Dual Descent for Network Optimization." Papers of the 2011 American Control Conference, June 29-July 01, 2011, San Francisco, CA, USA.
Author's final manuscript
INSPEC Accession Number: 12338424