Publications

E. M. Gertz,, "A Quasi-Newton Trust-Region Method," Preprint ANL/MCS-P873-0201, February 2001. [pdf]

The classical trust-region method for unconstrained minimization can be augmented with a line search that finds a point that satisfies the Wolfe conditions. One can use this new method to define an algorithm that simultaneously satisfies the quasi-Newton condition at each iteration and maintains a positive-definite approximation to the Hessian of the objective function. This new algorithm has strong global convergence properties and appears to be robust and
efficient in practice.