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A numerically robust hybrid steepest descent method for the convexly constrained generalized inverse problems. (English) Zbl 1039.47051
Nashed, M. Zuhair (ed.) et al., Inverse problems, image analysis, and medical imaging. AMS special session on interaction of inverse problems and image analysis, New Orleans, LA, USA, January 10–13, 2001. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-2979-3/pbk). Contemp. Math. 313, 269-305 (2002).
The aim of this paper is to show that (1) various algorithmic solutions to convexly constrained generalized inverse problems may be obtained in a unified manner from a certain hybrid steepest descent method, and (2) some particular versions of this method are gifted with notable robustness to the numerical errors. The obtained facts extend some recent contributions due to N. Ogura and I. Yamada [Numer. Funct. Anal. Optimization 23, 113–137 (2002; Zbl 1178.90346)].
For the entire collection see [Zbl 1003.00013].

##### MSC:
 47J25 Iterative procedures involving nonlinear operators 47J07 Abstract inverse mapping and implicit function theorems involving nonlinear operators 47H10 Fixed-point theorems 90C25 Convex programming 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 90C30 Nonlinear programming