The q-Levenberg-Marquardt method for unconstrained nonlinear optimization

Abstract: A q-Levenberg-Marquardt method is an iterative procedure that blends a q-steepest descent and q-Gauss-Newton methods. When the current solution is far from the correct one the algorithm acts as the q-steepest descent method. Otherwise the algorithm acts as the q-Gauss-Newton method. A damping parameter is used to interpolate between these two methods. The q-parameter is used to escape from local minima and to speed up the search process near the optimal solution.