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**Minimization of Tikhonov functionals in Banach spaces.**
*(English)*
Zbl 1357.49135

Summary: Tikhonov functionals are known to be well suited for obtaining regularized solutions of linear operator equations. We analyze two iterative methods for finding the minimizer of norm-based Tikhonov functionals in Banach spaces. One is the steepest descent method, whereby the iterations are directly carried out in the underlying space, and the other one performs iterations in the dual space. We prove strong convergence of both methods.

### MSC:

49N45 | Inverse problems in optimal control |

47N10 | Applications of operator theory in optimization, convex analysis, mathematical programming, economics |

49N20 | Periodic optimal control problems |

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\textit{T. Bonesky} et al., Abstr. Appl. Anal. 2008, Article ID 192679, 19 p. (2008; Zbl 1357.49135)

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### References:

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