Improved Hessian approximations for the limited memory BFGS method

This paper considers simple modifications of the limited memory BFGS (L-BFGS) method for large scale optimization. It describes algorithms in which alternating ways of re-using a given set of stored difference vectors are outlined. The proposed algorithms resemble the L-BFGS method, except that the initial Hessian approximation is defined implicitly like the L-BFGS Hessian in terms of some stored vectors rather than the usual choice of a multiple of the unit matrix. Numerical experiments show that the new algorithms yield desirable improvement over the L-BFGS method.