A progression strategy of proximal algorithm for the unconstrained optimization

In order to accurately solve the unconstrained optimization problem in which the objective function is nonlinear, a new optimization method different from both linear search and trust region is presented in this paper. This new method is based on the family of proximal algorithms. We customize our algorithm to solve different unconstrained optimization problems, and we verify the theoretical of the proposed method via different numerical examples where we compare the new algorithm with some existing state-of-the-art algorithms. Finally the simulation results proved the performance of the algorithm and indicates the advantage of the proposed algorithm in the case where the hypotheses are verified.