A new approach to nonlinear constrained Tikhonov regularization

Details A new approach to nonlinear constrained Tikhonov regularization A new approach to nonlinear constrained Tikhonov regularization

2011-09-03

arxiv.org/abs/1109.0654v1

Mathematics

Numerical Analysis

21 pages, to appear in Inverse Problems

Scientific paper

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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