Maximal flow through a domain

It is proved that, if the DFP or BFGS algorithm with step-lengths of one is applied to a functionF(x) that has a Lipschitz continuous second derivative, and if the calculated vectors of variables converge to a point at which ?F is zero and ?² F is positive definite, then the sequence of variable metric matrices also converges. The limit of this sequence is identified in the case whenF(x) is a strictly convex quadratic function.