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Distributed optimization is an essential paradigm to solve large-scaleoptimization problems in modern applications where big-data andhigh-dimensionality creates a computational bottleneck. Distributedoptimization algorithms that exhibit fast convergence allow us to fully utilizecomputing resources and effectively scale to larger optimization problems in amyriad of areas ranging from machine learning to power systems. In this work,we introduce a new centralized distributed optimization algorithm (ECADO)inspired by an equivalent circuit model of the distributed problem. Theequivalent circuit (EC) model provides a physical analogy to derive newinsights to develop a fast-convergent algorithm. The main contributions of thisapproach are: 1) a weighting scheme based on a circuit-inspired aggregatesensitivity analysis, and 2) an adaptive step-sizing derived from a stable,Backward-Euler numerical integration. We demonstrate that ECADO exhibits fasterconvergence compared to state-of-the art distributed optimization methods andprovably converges for nonconvex problems. We leverage the ECADO features tosolve convex and nonconvex optimization problems with large datasets such as:distributing data for logistic regression, training a deep neural network modelfor classification, and solving a high-dimensional problem security-constrainedoptimal power flow problem. Compared to state-of-the-art centralized methods,including ADMM, centralized gradient descent, and DANE, this new ECADO approachis shown to converge in fewer iterations.

An Equivalent Circuit Approach to Distributed Optimization