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The convergence of variable metric matrices in unconstrained optimization. (English) Zbl 0532.49015

The authors address the question of convergence of the sequence of variable metric matrices for certain quasi-Newton algoritms in unconstrained optimization. It is assumed that the objective function has a Lipschitz continuous derivative and a positive definite Hessian at the limit point of the iterates. Then, for the DFP- and BFGS-method with unit step length, the sequence of update matrices converges to a limit.
Reviewer: E.Sachs

MSC:

49M15 Newton-type methods
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
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References:

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