A descent algorithm for nonsmooth convex optimization - Fukushima, Masao (Mathematical programming, 1984)
This paper presents a new descent algorithm for minimizing a convex function which is not necessarily differentiable. The algorithm can be implemented and may be considered a modification of the epsilon -subgradient algorithm and Lemarechal's descent algorithm. Also our algorithm is seen to be closely related to the proximal point algorithm applied to convex minimization problems. A convergence theorem for the algorithms is established under the assumption that the objective function is bounded from below. Limited computational experience with the algorithm is also reported.