Abstract
Assume that F is a nonlinear operator on a real Hilbert space H which is η-strongly monotone and κ-Lipschitzian on a nonempty closed convex subset C of H. Assume also that C is the intersection of the fixed point sets of a finite number of nonexpansive mappings on H. We devise an iterative algorithm which generates a sequence (x n ) from an arbitrary initial point x 0∈H. The sequence (x n ) is shown to converge in norm to the unique solution u* of the variational inequality
Applications to constrained pseudoinverse are included.
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Xu, H.K., Kim, T.H. Convergence of Hybrid Steepest-Descent Methods for Variational Inequalities. Journal of Optimization Theory and Applications 119, 185–201 (2003). https://doi.org/10.1023/B:JOTA.0000005048.79379.b6
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DOI: https://doi.org/10.1023/B:JOTA.0000005048.79379.b6