Minimizing locally Lipschitz functions via bundle trust region algorithms – Najmeh Hoseini Monjezi

Nonsmooth optimization arises in many real life applications, for instance, in the fields of the optimal shape design, economics, mechanics, data mining and machine learning. Along with the nonsmooth nature, many practical applications have nonconvex structure and due to this, the numerical computation of their solutions is more challenging. In this talk, we discuss a bundle trust region algorithm for solving nonsmooth nonconvex optimization problems from both practical and theoretical points of view. Based on the bundle methods the objective function is approximated by a piecewise linear working model which is updated by adding cutting planes at unsuccessful trial steps. The algorithm defines, at each iteration, a new trial point by solving a subproblem that employs the working model in the objective function subject to a region, which is called the trust region. Under a lower-C1 assumption on the objective function, global convergence of the proposed algorithm is verified to stationary points. At the end, in order to demonstrate the reliability and efficiency of the proposed algorithm, a summery of numerical experiments are reported.