An effective nonsmooth optimization algorithm for locally Lipschitz functions

To construct an effective minimization algorithm for locally Lipschitz functions, we show how to compute a descent direction satisfying Armijoʹs condition. We present a finitely terminating algorithm to construct an approximating set for the 􀁈 -subdifferential leading to the desired descent direction. Using this direction, we propose a minimization algorithm for locally Lipschitz functions and prove its convergence. Finally, we implement our algorithm with MATLAB codes and report our result