Weak subgradient method with path based target level algorithm for nonconvex optimization

We study a new version of the weak subgradient method, recently developed by Dinc Yalcin and Kasimbeyli for solving nonsmooth, nonconvex problems. This method is based on the concept of using any weak subgradient of the objective of the problem at the currently generated point with a version of the dynamic stepsize in order to produce a new point at each iteration. The target value needed in the dynamic stepsize is defined using a path based target level (PBTL) algorithm to ensure the optimal value of the problem is reached. We analyze the convergence and give an estimate of the convergence rate of the proposed method. Furthermore, we demonstrate the performance of the proposed method on nonsmooth, nonconvex test problems, and give the computational results by comparing them with the approximately optimal solutions.