A new nonmonotone line search method for nonsmooth nonconvex optimization

In this paper, we develop a nonmonotone line search strategy for minimization of the locally Lipschitz functions. First, the descent direction (DD) is defined based on ∂ϵf(⋅) where ϵ>0. Next, we introduce a minimization algorithm to find a step length along the DD satisfying the nonsmooth nonmonotone Armijo condition. Choosing an adequate step length is the main purpose of the classic nonmonotone line search methods for a given DD, while in this paper both a search direction and step length are simultaneously computed. The global convergence of the minimization algorithm is proved by some assumptions on the DD. Finally, the proposed algorithm is implemented in the MATLAB environment and compared with another existing nonsmooth algorithm on some nonconvex nonsmooth optimization test problems. The efficiency of the proposed algorithm is shown by numerical results in solving some small-scale and large-scale nonsmooth optimization test problems.