Theoretical and numerical comparison of first order algorithms for cocoercive equations and smooth convex optimization

This paper provides a theoretical and numerical comparison of classical first-order splitting methods for solving smooth convex optimization problems cocoercive equations. From point view, we compare convergence rates gradient descent, forward-backward, Peaceman-Rachford, Douglas-Rachford algorithms minimizing the sum two functions when one them is strongly convex. A similar given in more general setting under presence strong monotonicity observe that are strictly better than corresponding equations some algorithms. We obtain improved with respect to literature several instances by exploiting structure our problems. Moreover, indicate which algorithm has smallest rate depending on convexity parameters. verify results implementing comparing previous well established signal image inverse involving sparsity. replace widely used ?1 norm Huber loss fully proximal-based strategies have advantages using steps.