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Title: Distributed Approximate Newton Algorithms and Weight Design for Constrained Optimization

Abstract

Motivated by economic dispatch and linearly-constrained 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 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 algorithms with our weight design have superior convergence properties compared to existing weighting strategies for first-order saddle-point and gradient descent methods.

Authors:
 [1];  [2];  [1]
  1. University of California, San Diego
  2. 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 Agency-Energy (ARPA-E)
OSTI Identifier:
1566052
Report Number(s):
NREL/JA-5D00-74927
DOE Contract Number:  
AC36-08GO28308
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; multi-agent systems; resource allocation; networked systems; second-order methods

Citation Formats

Anderson, Tor, Chang, Chin-Yao, 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, Chin-Yao, & Martinez, Sonia. Distributed Approximate Newton Algorithms and Weight Design for Constrained Optimization. United States. doi:10.1016/j.automatica.2019.108538.
Anderson, Tor, Chang, Chin-Yao, 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, Chin-Yao and Martinez, Sonia},
abstractNote = {Motivated by economic dispatch and linearly-constrained 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 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 algorithms with our weight design have superior convergence properties compared to existing weighting strategies for first-order saddle-point and gradient descent methods.},
doi = {10.1016/j.automatica.2019.108538},
journal = {Automatica},
number = ,
volume = 109,
place = {United States},
year = {2019},
month = {9}
}