A Smooth Method for Solving Non-Smooth Unconstrained Optimization Problems

We consider unconstrained optimization problems using the expensive objective function in which the derivatives are not available. This property of problems can often impede the performance of optimization algorithms. Most algorithms usually determine a Quasi-Newton direction and then use line search technique. We propose a smoothing algorithm which is developed to modify trust region and to handle the objective function based on radial basis functions (RBFs). The value of objective function is reduced according to the relation with the predicted reduction of surrogate model. At each iteration we construct the quadratic model based on RBFs. The global convergence of the proposed method is studied. The numerical results are presented for some standard test problem to validate the theoretical results.