Reduced-Hessian quasi-Newton methods for unconstrained optimization (Q2784409)

The authors develop a reduced Hessian quasi-Newton method with combined reinitialization and lingering for unconstrained optimization problems. The algorithm forces the iterates to stay on an appropriate manifold of a dimension much smaller than that of the reduced Hessian itself and reinitializes approximate curvature along directions off the manifold. In this way, typical difficulties associated with ill-conditioned or poor initial estimates can be overcome. Extensive numerical results document the efficiency and robustness of the approach.