Global Convergence of a Closed‐Loop Regularized Newton Method for Solving Monotone Inclusions in Hilbert Spaces

Global Convergence of a Closed‐Loop Regularized Newton Method for Solving Monotone Inclusions in Hilbert Spaces

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Article ID: iaor20132855
Volume: 157
Issue: 3
Start Page Number: 624
End Page Number: 650
Publication Date: Jun 2013
Journal: Journal of Optimization Theory and Applications
Authors: , ,
Keywords: heuristics
Abstract:

We analyze the global convergence properties of some variants of regularized continuous Newton methods for convex optimization and monotone inclusions in Hilbert spaces. The regularization term is of Levenberg–Marquardt type and acts in an open‐loop or closed‐loop form. In the open‐loop case the regularization term may be of bounded variation.

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