Convergence of Hybrid Steepest-Descent Methods for Variational Inequalities

H. K. Xu and T. H. Kim
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H. K. Xu: University of Durban-Westville
T. H. Kim: Pukyong National University

Journal of Optimization Theory and Applications, 2003, vol. 119, issue 1, No 12, 185-201

Abstract: 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 $$\left\langle {F(u*),\user1{v} - u*} \right\rangle \geqslant 0$$ Applications to constrained pseudoinverse are included.

Keywords: Iterative algorithms; hybrid steepest-descent methods; convergence; nonexpansive mappings; Hilbert space; constrained pseudoinverses (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (22)

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DOI: 10.1023/B:JOTA.0000005048.79379.b6

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