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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)].
MSC:
47J25Iterative procedures (nonlinear operator equations)
47J07Abstract inverse mapping and implicit function theorems
47H10Fixed point theorems for nonlinear operators on topological linear spaces
90C25Convex programming
47H09Mappings defined by “shrinking” properties
90C30Nonlinear programming