Distributed Approximate Newton Algorithms and Weight Design for Constrained Optimization

Journal Article · Fri Sep 06 04:00:00 EDT 2019 · Automatica

DOI:https://doi.org/10.1016/j.automatica.2019.108538· OSTI ID:1566052

Anderson, Tor ^[1]; Chang, Chin-Yao ^[2]; Martinez, Sonia ^[1]

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1. University of California, San Diego
2. National Renewable Energy Laboratory (NREL), Golden, CO (United States)

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.

• Research Organization: National Renewable Energy Laboratory (NREL), Golden, CO (United States)
• Sponsoring Organization: U.S. Department of Energy, Advanced Research Projects Agency-Energy (ARPA-E)
• DOE Contract Number: AC36-08GO28308
• OSTI ID: 1566052
• Report Number(s): NREL/JA-5D00-74927
• Journal Information: Automatica, Journal Name: Automatica Vol. 109
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
distributed optimization
multi-agent systems
networked systems
resource allocation
second-order methods