# A Globally Convergent Penalty-Based Gauss-Newton Algorithm with Applications

## TL;DR

This paper introduces a globally convergent Gauss-Newton algorithm for non-convex, non-smooth optimization problems, demonstrating its effectiveness on power flow problems and achieving comparable performance to established solvers.

## Contribution

The paper develops a novel penalty-based Gauss-Newton algorithm with proven global and local convergence properties for non-smooth optimization problems.

## Key findings

- Global convergence to stationary points from any initial point
- Local quadratic convergence under certain conditions
- Comparable performance to IPOPT on power flow problems

## Abstract

We propose a globally convergent Gauss-Newton algorithm for finding a local optimal solution of a non-convex and possibly non-smooth optimization problem. The algorithm that we present is based on a Gauss-Newton-type iteration for the non-smooth penalized formulation of the original problem. We establish a global convergence rate for this scheme from any initial point to a stationary point of the problem while using an exact penalty formulation. Under some more restrictive conditions we also derive local quadratic convergence for this scheme. We apply our proposed algorithm to solve the Alternating Current optimal power flow problem on meshed electricity networks, which is a fundamental application in power systems engineering. We verify the performance of the proposed method by showing comparable behavior with IPOPT, a well-established solver. We perform our validation on several representative instances of the optimal power flow problem, which are sourced from the MATPOWER library.