Minimization of the Tikhonov functional in Banach spaces smooth and convex of power type by steepest descent in the dual

Minimization of the Tikhonov functional in Banach spaces smooth and convex of power type by steepest descent in the dual

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Article ID: iaor20113687
Volume: 48
Issue: 2
Start Page Number: 309
End Page Number: 324
Publication Date: Mar 2011
Journal: Computational Optimization and Applications
Authors:
Keywords: steepest descent, Banach space
Abstract:

For Tikhonov functionals of the form Ψ(x)=∥Ax-y∥ Y r +α∥x∥ X q we investigate a steepest descent method in the dual of the Banach space X. We show convergence rates for the proposed method and present numerical tests.

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