Correction of trust region method with a new modified Newton method

One of the iterative techniques for solving unconstrained minimization problems is trust region method. Trust region methods are robust and can be applied to ill-conditioned problems. In this paper, we give a new nonmonotone trust region algorithm to solve problems arising from unconstrained optimization. The curvilinear paths we set are dogleg paths, generated mainly by employing Q.I.F. factorization (Quadrant Interlocking Factorisation) for general symmetric matrices which may be indefinite. Convergence properties of the trust region algorithm are given. Moreover, numerical experiments show that the new algorithm is competitive with some existing methods and performs very well.