A Hybrid Algorithm for Practical Nonconvex Optimization

This paper proposes a hybrid algorithm for optimization, to ensure convergence to a local minimimzer of a nonconvex Morse objective function L with a single, scalar argument. Developed using hybrid system tools, and based on the heavy ball method, the algorithm features switching strategies to detect whether the state is near a critical point and enable escape from local maximizer, using measurements of the gradient of L. Key properties of the resulting closed-loop system, including existence of solutions and practical global attractivity, are revealed. Numerical results validate the findings. Copyright (C) 2021 The Authors.