A novel switched systems approach to nonconvex optimisation

TL;DR

This paper introduces a new switched systems method for nonconvex optimization that converges to KKT points, emphasizing lower dimensionality by focusing solely on primal variables, and demonstrates its effectiveness on various complex problems.

Contribution

The paper presents a novel switching dynamics approach that reduces dimensionality and converges to KKT points in nonconvex optimization, with practical applications shown.

Findings

Effective convergence to KKT points demonstrated.

Lower dimensionality compared to traditional methods.

Successful application to diverse nonconvex problems.

Abstract

We develop a novel switching dynamics that converges to the Karush-Kuhn-Tucker (KKT) point of a nonlinear optimisation problem. This new approach is particularly notable for its lower dimensionality compared to conventional primal-dual dynamics, as it focuses exclusively on estimating the primal variable. Our method is successfully illustrated on general quadratic optimisation problems, the minimisation of the classical Rosenbrock function, and a nonconvex optimisation problem stemming from the control of energy-efficient buildings.