Chin-Yao Chang

Weight design of distributed approximate Newton algorithms for constrained optimization

This paper presents a distributed algorithm to solve an economic dispatch problem, which takes the form of a linearly-constrained resource allocation problem. Distributed gradient-based methods are commonly used to solve problems of this form, which inherit slow convergence. The Newton method is a centralized alternative which uses second-order information to provide faster convergence. However, computing a Newton step is difficult in distributed settings and typically requires all-to-all agent communication. In this paper, we propose the distributed approx-Newton algorithm to approximate the Newton step with only distributed communication. The convergence of this algorithm is discussed and rigorously analyzed. In addition, we aim to address the problem of designing communication topologies and weightings that are optimal for second-order methods. To this end, we propose an effective approximation which is loosely based on completing the square to address the NP-hard bilinear optimization involved in the design. Simulations demonstrate that our proposed weight design applied to the distributed approx-Newton algorithm has a superior convergence property compared to existing gradient-inspired weight design applied to the Distributed Gradient Descent method.

A scheduled-asynchronous distributed optimization algorithm for the optimal power flow problem

Optimal power flow (OPF) problems are non-convex and large-scale optimization problems. Finding an optimal solution for the OPF problem in real time is challenging and important in various applications. Recent studies show that a wide class of OPF problems have an exact semidefinite programming (SDP) convex relaxation. However, only few works have considered distributed algorithms to solve these. In this paper, we propose a scheduled-asynchronous algorithm with this objective. The proposed algorithm follows an ADMM-like iteration for every edge in the electrical network and is asynchronous in the sense that the agents do not simultaneously update their local variables, but only do so when they have received fresh information from all of their neighbors. In addition, if the electrical network topology is bipartite, the proposed algorithm has a convergence rate of O(1/n), where n is the iteration per agent. The asynchronous property and fast convergence rate make the proposed algorithm suitable for the OPF problem. Simulation studies demonstrate that the proposed algorithm is scalable with the number of buses and robust to network effects including delays and packet drops.