Trust region dogleg path algorithms for unconstrained minimization

In this paper, we propose a class of convenient curvilinear search algorithms to solve trust region problems arising from unconstrained optimization. The curvilinear paths we set are dogleg paths, generated mainly by employing Bunch–Parlett factorization for general symmetric matrices which may be indefinite. These algorithms are easy to use and globally convergent. It is proved that these algorithms satisfy the first- and second-order stationary point convergence properties and that the convergence rate is quadratic under commonly used conditions.