# The convergence of variable metric matrices in unconstrained optimization

@article{Ge1983TheCO, title={The convergence of variable metric matrices in unconstrained optimization}, author={Renpu Ge and M. J. D. Powell}, journal={Mathematical Programming}, year={1983}, volume={27}, pages={123-143} }

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 ∇2F 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.

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