Hybrid spectral gradient method for the unconstrained minimization problem

摘要

We present a hybrid algorithm that combines a genetic algorithm with the Barzilai-Borwein gradient method. Under specific assumptions the new method guarantees the convergence to a stationary point of a continuously differentiable function, from any arbitrary initial point. Our preliminary numerical results indicate that the new methodology finds efficiently and frequently the global minimum, in comparison with the globalized Barzilai-Borwein method and the genetic algorithm of the Toolbox of Genetic Algorithms of MatLab.