An extension of the quasi-Newton method for minimizing locally Lipschitz functions

We present a method to minimize locally Lipschitz functions. At first, a local quadratic model is developed to approximate a locally Lipschitz function. This model is constructed by using the ϵ-subdifferential. We minimize this local model and compute a search direction. It is shown that this direction is descent. We generalize the Wolfe conditions for finding an adequate step length along this direction. Next, the method is equipped with a quasi Newton approach to update the local model and its globally convergence is proposed. Finally, the proposed algorithm is implemented in MATLAB environment on some standard nonsmooth optimization test problems and compared with some algorithms in the literature.