A quasi-Newton trust-region method
For nonlinear multivariate unconstrained optimization the quasi-Newton technique is used quite often, especially in those cases where the Hessian is either not known analytically or expensive to compute. E. Michael Gertz offers an approach which is based on the quasi-Newton method, but augmented with a line-search method to find a point that satisfies the Wolfe conditions. The algorithm suggested by Gertz is an improved optimization algorithm that simultaneously satisfies the quasi-Newton condition at each iteration and maintains a positive-definite approximation to the Hessian of the objective function. Futhermore, the author proofs that the new algorithm has strong global convergence properties and is robust and efficient in practice. An additionally conducted series of numerical tests compares three alternative optimization algorithms: the Wolfe-LS (Wolfe Line Search algorithm), the Wolfe-TR (Wolfe Trust Region Algorithm) and the biased-TR. Out of 33 problems solved by all the selected algorithms, the biased-TR algorithm shows up with the best overall performance.
scientific article; zbMATH DE number 2111481