  Distributed optimization is an essential paradigm to solve large-scale
optimization problems in modern applications where big-data and
high-dimensionality creates a computational bottleneck. Distributed
optimization algorithms that exhibit fast convergence allow us to fully utilize
computing resources and effectively scale to larger optimization problems in a
myriad 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. The
equivalent circuit (EC) model provides a physical analogy to derive new
insights to develop a fast-convergent algorithm. The main contributions of this
approach are: 1) a weighting scheme based on a circuit-inspired aggregate
sensitivity analysis, and 2) an adaptive step-sizing derived from a stable,
Backward-Euler numerical integration. We demonstrate that ECADO exhibits faster
convergence compared to state-of-the art distributed optimization methods and
provably converges for nonconvex problems. We leverage the ECADO features to
solve convex and nonconvex optimization problems with large datasets such as:
distributing data for logistic regression, training a deep neural network model
for classification, and solving a high-dimensional problem security-constrained
optimal power flow problem. Compared to state-of-the-art centralized methods,
including ADMM, centralized gradient descent, and DANE, this new ECADO approach
is shown to converge in fewer iterations.
