Approximate Gaussian distributions in optimization by random perturbation methods Original Research Article

In previous works, we have developed algorithms based on random perturbations of usual descent methods for the optimization of differentiable non-convex functions. These algorithms have been shown to be effective when applied to significant problems of Mechanical Engineering. The perturbation is generally Gaussian, since mathematical results of convergence can be established in this particular case. These results concern the convergence of the generated distributions to a distribution concentrated on the minima of the functional. In the field of convergence of distributions, the works of Tsallis suggest that the efficiency can be increased for some particular problems. This work investigates this point and considers approximations suggested by Tsallis as alternatives to the usual Gaussian variables.