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URN etd-0626106-210644
Author Wei-ling Huang
Author's Email Address m932040026@student.nsysu.edu.tw
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Department Applied Mathematics
Year 2005
Semester 2
Degree Master
Type of Document
Language English
Title Hybrid Steepest-Descent Methods for Variational Inequalities
Date of Defense 2006-05-26
Page Count 32
Keyword
  • convergence
  • Iterative algorithms
  • constrained generalized pseudoinverse
  • hybrid steepest-descent methods with variable parameters
  • nonexpansive mappings
  • Hilbert space
  • Abstract Assume that F is a nonlinear operator on a real Hilbert space H which is strongly monotone and 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 make a slight modification of the iterative algorithm in Xu and Kim (Journal of Optimization Theory and Applications, Vol. 119, No. 1, pp. 185-201, 2003), which generates a sequence {xn} from an arbitrary initial point x0 in H. The sequence {xn} is shown to converge in norm to the unique solution u* of the variational inequality, under the conditions different from Xu and Kim’s ones imposed on the parameters. Applications to constrained generalized pseudoinverse are included. The results presented in this paper are complementary ones to Xu and Kim’s theorems (Journal of Optimization Theory and Applications, Vol. 119, No. 1, pp. 185-201, 2003).
    Advisory Committee
  • Y. C. Lin - chair
  • S. Huang - co-chair
  • Jen-chih Yao - advisor
  • Mu-ming Wong - advisor
  • Files
  • etd-0626106-210644.pdf
  • indicate access worldwide
    Date of Submission 2006-06-26

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