A quasi-Newton based pattern search algorithm for unconstrained optimization

This study proposes a new robust quasi-Newton algorithm for unconstrained optimization problem. The factorization of approximating Hessian matrices is investigated to provide a series of positive bases for pattern search. Experiments on some well-known optimization test problems are presented to show the efficiency and robustness of the proposed algorithm. It is found that the proposed algorithm is competitive and outperforms some other derivative-free algorithms.