A new quasi-Newton pattern search method based on symmetric rank-one update for unconstrained optimization

This paper proposes a new robust and quickly convergent pattern search method based on an implementation of OCSSR1 (Optimal Conditioning Based Self-Scaling Symmetric Rank-One) algorithm [M.R. Osborne, L.P. Sun, A new approach to symmetric rank-one updating, IMA Journal of Numerical Analysis 19 (1999) 497–507] for unconstrained optimization. This method utilizes the factorization of approximating Hessian matrices to provide a series of convergent positive bases needed in pattern search process. Numerical experiments on some famous optimization test problems show that the new method performs well and is competitive in comparison with some other derivative-free methods.