Generating conjugate directions without line searches using factorized variable metric updating formulas

Donald Goldfarb

Abstract: It is shown how to generate conjugate directions without exact line searches by applying variable metric updating formulas in factorized form to give the columns of the Cholesky factors of the Hessian matrix one at a time. Minimization methods based upon these results are given, including one which can take advantage of sparsity in the matrix of second derivatives of the objective function. The results of some numerical tests on a small sample of test problems are presented.