Title page for etd-0630113-233126


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URN etd-0630113-233126
Author Han-Ting Hsu
Author's Email Address No Public.
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Department Applied Mathematics
Year 2012
Semester 2
Degree Master
Type of Document
Language English
Title Iterative gradient methods for constrained minimization
Date of Defense 2013-07-08
Page Count 19
Keyword
  • projection
  • gradient projection method
  • iteration
  • algorithm
  • fixed point
  • convergence
  • constrained minimization
  • contraction
  • nonexpansive mapping
  • Abstract In this paper we deal with the problem of minimizing a strongly convex objective function over the set of fixed points of a nonexpansive mapping T. This extends the constrained strongly convex minimization problem over a closed convex subset C of a Hilbert space since the projection Pc is nonexpansive. By introducing a parameter λ>0 , we define a family of contractions Tλ, each of which has a unique fixed point denoted as ξλ. We first prove that as λ→0, ξλ converges in norm to the unique solution of our minimization problem. We then introduce an iteration algorithm by discretization of the mappings Tλ, and prove strong convergence of this algorithm under appropriate conditions imposed on the sequence of parameters of the algorithm.
    Advisory Committee
  • Lai-Jiu Lin - chair
  • Ngai-Ching Wong - co-chair
  • Jen-Chih Yao - advisor
  • Hong-Kun Xu - advisor
  • Files
  • etd-0630113-233126.pdf
  • Indicate in-campus at 1 year and off-campus access at 1 year.
    Date of Submission 2013-07-31

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