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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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