Specular gradient methods for nonsmooth convex optimization in Euclidean spaces: a subgradient selection strategy

Abstract

This paper deals with nonsmooth convex optimization problems in Euclidean spaces. We identify special elements of the subdifferential of a convex function, called specular gradients. Based on this observation, we propose three numerical methods that use specular gradients in subgradient methods. We prove the convergence of the proposed methods under suitable step sizes. Numerical experiments demonstrate that the proposed methods are capable of minimizing non-differentiable functions that classical methods fail to minimize.