Title page for etd-0602111-000058


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URN etd-0602111-000058
Author Yen-Ling Chen
Author's Email Address No Public.
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Department Applied Mathematics
Year 2010
Semester 2
Degree Master
Type of Document
Language English
Title Iterative Methods for Minimization Problems over Fixed Point Sets
Date of Defense 2010-06-17
Page Count 27
Keyword
  • Halpern's algorithm
  • demiclosedness principle
  • hybrid method
  • quadratic optimization
  • strongly monotone
  • monotone mapping
  • projection
  • iterative method
  • fixed point
  • nonexpansive mapping
  • Minimization
  • Abstract In this paper we study through iterative methods the minimization problem
                  min_{x∈C} Θ(x)                  (P)
    where the set C of constraints is the set of fixed points of a nonexpansive mapping T in a real Hilbert space H, and the objective function Θ:H→R is supposed to be continuously Gateaux dierentiable. The gradient projection method for solving problem (P) involves with the projection P_{C}. When C = Fix(T), we provide a
    so-called hybrid iterative method for solving (P) and the method involves with the mapping T only. Two special cases are included: (1) Θ(x)=(1/2)||x-u||^2 and (2) Θ(x)=<Ax,x> - <x,b>. The first case corresponds to finding a fixed point of T which is closest to u from the fixed point set Fix(T). Both cases have received a lot of investigations recently.
    Advisory Committee
  • Lai-Jiu Lin - chair
  • Jen-Chih Yao - co-chair
  • Ngai-Ching Wong - co-chair
  • Hong-Kun Xu - advisor
  • Files
  • etd-0602111-000058.pdf
  • indicate access worldwide
    Date of Submission 2011-06-02

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