A NEW NONSMOOTH TRUST-REGION METHOD EQUIPPED WITH A LINE SEARCH FOR MINIMIZING LOCALLY LIPSCHITZ FUNCTIONS

In this paper, we employ a line search technique in the framework of trust region methods and propose a new nonsmooth trust region method for minimization of locally Lipschitz functions. Despite existing nonsmooth trust region methods, our new proposed approach performs a line search along a descent direction rather than re-solving the subproblem in the lack of sufficient reduction. This causes a significant decrease in the number of subproblem that need to be solved and, consequently, a decrease in the number of function evaluations. Under some standard assumptions, the global convergence property of the new proposed method is established for minimization of locally Lipschitz functions. The proposed algorithm is implemented in MATLAB environment and applied on some test problems. Numerical results confirm the efficiency of the new approach in comparison with some existing trust region methods for nonsmooth functions.