The Shanno-Toint Procedure for Updating Sparse Symmetric Matrices

Two recent methods (Shanno, 1978; Toint, 1980) for revisingestimates of sparse second derivative matrices in quasi-Newtonoptimization algorithms reduce to variable metric formulae whenthere are no sparsity conditions. It is proved that these methodsare equivalent. Further, some examples are given to show thatthe procedure may make the second derivative approximationsworse when the objective function is quadratic. Therefore theconvergence properties of the procedure are sometimes less goodthan the convergence properties of other published methods forrevising sparse second derivative approximations.