Convergence of Hybrid Steepest-Descent Methods for Variational Inequalities

@article{Xu2003ConvergenceOH,
title={Convergence of Hybrid Steepest-Descent Methods for Variational Inequalities},
author={H. Xu and T. Kim},
journal={Journal of Optimization Theory and Applications},
year={2003},
volume={119},
pages={185-201}
}
• Published 2003
• Mathematics
• Journal of Optimization Theory and Applications
AbstractAssume 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 (xn) from an arbitrary initial point x0∈H. The sequence (xn) is shown to converge in norm to the unique solution u* of the variational inequality \left\langle… Expand
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