A proximal regularization of the steepest descent method

The authors introduce a quadratic regularization term (in the spirit of the proximal point method) in the line searches of the steepest descent method, obtaining thus better convergence results. While the convergence analysis of the steepest descent method requires bounded level sets of the minimand to get a bounded sequence, and establishes, even for convex objectives, only optimality of the cluster points, the present approach guarantees convergence of the whole sequence to a minimizer when the objective function is pseudo-convex, whether its level sets are bounded or not.