Some Numerical Experiments with Variable Storage Quasi-Newton Algorithms

Gilbert, J.C. & Lemarechal, C. (1988). Some Numerical Experiments with Variable Storage Quasi-Newton Algorithms. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-88-121

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Abstract

This paper relates some numerical experiments with variable storage quasi-Newton methods for the optimization of large-scale models. The basic idea of the recommended algorithm is to start bfgs updates on a diagonal matrix, itself generated by an update formula and adjusted to Rayleigh's ellipsoid of the local Hessian of the objective function in the direction of the change in the gradient.

A variational derivation of some rank one and rank two updates in Hilbert spaces is also given.

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