Title page for etd-0626110-101550


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URN etd-0626110-101550
Author Yen-Ru Lin
Author's Email Address No Public.
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Department Applied Mathematics
Year 2009
Semester 2
Degree Master
Type of Document
Language English
Title Projection Methods for Variational Inequalities
Governed by Inverse Strongly Monotone
Operators
Date of Defense 2010-06-17
Page Count 26
Keyword
  • fixed point
  • Variational inequality
  • Mann's algorithm
  • projection
  • monotone mapping
  • demiclosedness principle
  • Halpern's algorithm
  • nonexpansive mapping
  • inverse strongly monotone
  • strongly monotone
  • weak convergence
  • strongly convergence
  • Abstract Consider the variational inequality (VI)
    x* ∈C, ‹Fx*, x - x* ›≥0, x∈C (*)
    where C is a nonempty closed convex subset of a real Hilbert space H and
    F : C→ H is a monotone operator form C into H. It is known that if F is
    strongly monotone and Lipschitzian, then VI (*) is equivalently turned into
    a fixed point problem of a contraction; hence Banach's contraction principle
    applies. However, in the case where F is inverse strongly monotone, VI (*)
    is equivalently transformed into a fixed point problem of a nonexpansive
    mapping. The purpose of this paper is to present some results which apply
    iterative methods for nonexpansive mappings to solve VI (*). We introduce
    Mann's algorithm and Halpern's algorithm and prove that the sequences
    generated by these algorithms converge weakly and respectively, strongly to
    a solution of VI (*), under appropriate conditions imposed on the parameter
    sequences in the algorithms.
    Advisory Committee
  • Lai-Jiu Lin - chair
  • Jen-Chih Yao - co-chair
  • Ngai-Ching Wong - co-chair
  • Hong-Kun Xu - advisor
  • Files
  • etd-0626110-101550.pdf
  • indicate accessible in a year
    Date of Submission 2010-06-26

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