A modified filter-trust region algorithm and its global convergence properties for unconstrained optimization

In this paper, we propose a new filter-trust region algorithm for unconstrained optimization problems. A new filter technique is introduced to solve the problem when the direction d^k is not accepted. The theoretical analysis shows that the algorithm is not only global convergence but also R-linearly convergence and even super linearly convergence under some suitable conditions. Numerical results show that this method is effective in minimizing unconstrained optimization problems.