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A Levenberg-Marquardt method based on Sobolev gradients. (English) Zbl 1248.49040

Summary: We extend the theory of Sobolev gradients to include variable metric methods, such as the Newton method and the Levenberg–Marquardt method, as gradient descent iterations associated with stepwise variable inner products. In particular, we obtain existence, uniqueness, and asymptotic convergence results for a gradient flow based on a variable inner product.

MSC:

49M15 Newton-type methods
34H05 Control problems involving ordinary differential equations
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