Distributed Approximate Newton Algorithms and Weight Design for Constrained Optimization
Abstract
Motivated by economic dispatch and linearlyconstrained resource allocation problems, this paper proposes a class of novel 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 secondorder 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 approxNewton algorithm which converges linearly to the optimal solution for economic dispatch problems with unknown cost functions and relaxed local box constraints. For the full boxconstrained problem, we develop a continuous distributed approxNewton algorithm which is inspired by firstorder saddlepoint 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 constantsize communication messages, which lends itself to scalable implementations. Simulations demonstrate that the algorithms with our weight design have superior convergence properties compared to existing weighting strategies for firstorder saddlepoint and gradient descent methods.
 Authors:

 University of California, San Diego
 National Renewable Energy Laboratory (NREL), Golden, CO (United States)
 Publication Date:
 Research Org.:
 National Renewable Energy Lab. (NREL), Golden, CO (United States)
 Sponsoring Org.:
 U.S. Department of Energy, Advanced Research Projects AgencyEnergy (ARPAE)
 OSTI Identifier:
 1566052
 Report Number(s):
 NREL/JA5D0074927
 DOE Contract Number:
 AC3608GO28308
 Resource Type:
 Journal Article
 Journal Name:
 Automatica
 Additional Journal Information:
 Journal Volume: 109
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; distributed optimization; multiagent systems; resource allocation; networked systems; secondorder methods
Citation Formats
Anderson, Tor, Chang, ChinYao, and Martinez, Sonia. Distributed Approximate Newton Algorithms and Weight Design for Constrained Optimization. United States: N. p., 2019.
Web. doi:10.1016/j.automatica.2019.108538.
Anderson, Tor, Chang, ChinYao, & Martinez, Sonia. Distributed Approximate Newton Algorithms and Weight Design for Constrained Optimization. United States. doi:10.1016/j.automatica.2019.108538.
Anderson, Tor, Chang, ChinYao, and Martinez, Sonia. Fri .
"Distributed Approximate Newton Algorithms and Weight Design for Constrained Optimization". United States. doi:10.1016/j.automatica.2019.108538.
@article{osti_1566052,
title = {Distributed Approximate Newton Algorithms and Weight Design for Constrained Optimization},
author = {Anderson, Tor and Chang, ChinYao and Martinez, Sonia},
abstractNote = {Motivated by economic dispatch and linearlyconstrained resource allocation problems, this paper proposes a class of novel 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 secondorder 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 approxNewton algorithm which converges linearly to the optimal solution for economic dispatch problems with unknown cost functions and relaxed local box constraints. For the full boxconstrained problem, we develop a continuous distributed approxNewton algorithm which is inspired by firstorder saddlepoint 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 constantsize communication messages, which lends itself to scalable implementations. Simulations demonstrate that the algorithms with our weight design have superior convergence properties compared to existing weighting strategies for firstorder saddlepoint and gradient descent methods.},
doi = {10.1016/j.automatica.2019.108538},
journal = {Automatica},
number = ,
volume = 109,
place = {United States},
year = {2019},
month = {9}
}