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Distributed approximate Newton algorithms and weight design for constrained optimization.
- Source :
-
Automatica . Nov2019, Vol. 109, pN.PAG-N.PAG. 1p. - Publication Year :
- 2019
-
Abstract
- Motivated by economic dispatch and linearly-constrained resource allocation problems, this paper proposes a class of novel distributedapprox − Newton algorithms that approximate the standard Newton optimization method. We first develop the notion of an optimal edge weighting for the communication graph over which agents implement the second-order algorithm, and propose a convex approximation for the nonconvex weight design problem. We next build on the optimal weight design to develop a discrete distributed approx-Newton algorithm which converges linearly to the optimal solution for economic dispatch problems with unknown cost functions and relaxed local box constraints. For the full box-constrained problem, we develop a continuous distributed approx-Newton algorithm which is inspired by first-order saddle-point methods and rigorously prove its convergence to the primal and dual optimizers. A main property of each of these distributed algorithms is that they only require agents to exchange constant-size communication messages, which lends itself to scalable implementations. Simulations demonstrate that the distributedapprox − Newton algorithms with our weight design have superior convergence properties compared to existing weighting strategies for first-order saddle-point and gradient descent methods. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00051098
- Volume :
- 109
- Database :
- Academic Search Index
- Journal :
- Automatica
- Publication Type :
- Academic Journal
- Accession number :
- 138614128
- Full Text :
- https://doi.org/10.1016/j.automatica.2019.108538