Subgradient method for nonconvex nonsmooth optimization (Q353174)

Based on the notion of quasisecants introduced by \textit{A. M. Bagirov} and \textit{A. N. Ganjehlou} [Optim. Methods Softw. 25, No. 1, 3--18 (2010; Zbl 1202.65072)], the authors develop a version of the subgradient method for solving nonconvex nonsmooth optimization problems. Quasisecants are subgradients computed in some neighborhood of a point. The method contains a simple procedure for finding descent directions and for solving line search subproblems. The convergence of the method for a broad class of nonconvex nonsmooth optimization problems is proved. The results of numerical experiments demonstrate that this algorithm is a significant improvement of the subgradient method. The comparison of the method with proximal bundle methods are given as well.