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arXiv · 1109.0654

A new approach to nonlinear constrained Tikhonov regularization

Kazufumi Ito·Bangti Jin
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Abstract

We present a novel approach to nonlinear constrained Tikhonov regularization from the viewpoint of optimization theory. A second-order sufficient optimality condition is suggested as a nonlinearity condition to handle the nonlinearity of the forward operator. The approach is exploited to derive convergence rates results for a priori as well as a posteriori choice rules, e.g., discrepancy principle and balancing principle, for selecting the regularization parameter. The idea is further illustrated on a general class of parameter identification problems, for which (new) source and nonlinearity conditions are derived and the structural property of the nonlinearity term is revealed. A number of examples including identifying distributed parameters in elliptic differential equations are presented.

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Kazufumi Ito, Bangti Jin. 2011-09-03. A new approach to nonlinear constrained Tikhonov regularization. https://doi.org/10.1088/0266-5611%2F27%2F10%2F105005

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