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研究生:簡茵婷
研究生(外文):Yin-ting Chien
論文名稱:分裂可行性問題之迭代方法
論文名稱(外文):Iterative Approaches to the SplitFeasibility Problem
指導教授:徐洪坤
指導教授(外文):Hong-kun Xu
學位類別:碩士
校院名稱:國立中山大學
系所名稱:應用數學系研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2009
畢業學年度:97
語文別:英文
論文頁數:28
中文關鍵詞:CQ演算法梯度投影法絕對非擴張映射反強單調算子平均映射投影分裂可行性問題鬆弛CQ演算法
外文關鍵詞:firmly nonexpansive mappingrelaxed CQ algorithm.CQ algorithmgradient projectionalgorithmprojectionaveraged mappingSplit feasibility probleminverse strongly monotone operator
相關次數:
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摘要
在本論文中,我們將討論「分裂可行性問題」(SFP)之迭代方法。
我們從兩個角度來研究「CQ演算法」:最優化方法和固定點方法。前
者,我們應用梯度投影法證明其收斂性;後者,則用固定點演算法。
我們也研究「鬆弛CQ演算法」,其C和Q是凸函數的水平集合。因此,
我們提出一個收斂定理,並且提供一個較簡單的,有別於原作者Yang
[7] 的証明方法。
In this paper we discuss iterative algorithms for solving the split feasibility
problem (SFP). We study the CQ algorithm from two approaches: one
is an optimization approach and the other is a fixed point approach. We
prove its convergence first as the gradient-projection algorithm and secondly
as a fixed point algorithm. We also study a relaxed CQ algorithm in the
case where the sets C and Q are level sets of convex functions. In such case
we present a convergence theorem and provide a different and much simpler
proof compared with that of Yang [7].
Contents
1 Introduction 1
2 Preliminaries 3
3 The CQ algorithm 9
4 A relaxed CQ algorithm and its convergence 16
References 22
References
[1] C. Byrne, Iterative oblique projection onto convex subsets and the split feasibility
problem, Inverse Problems, 18 (2002), 441-453.
[2] C. Byrne, A unified treatment of some iterative algorithms in signal processing
and image reconstruction, Inverse Problems, 20 (2004), 103-120.
[3] Y. Censor and T. Elfving, A multiprojection algorithm using Bregman projections
in a priduct space, Numer. Algorithms 8 (1994), 221-239.
[4] K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, Cambridge
Studies in Advanced Mathematics, vol. 28, Cambridge University Press, 1990.
[5] A. Ruszczynski (2006), “Nonlinear optimization,” Princeton University Press.
[6] B. Qu and N. Xiu, A note on the CQ algorithm for the split feasibility problem,
Inverse Problems 21 (2005), 1655-1665.
[7] Q. Yang, The relaxed CQ algorithm for solving the split feasibility problem,
Inverse Problems 20 (2004), 1261-1266.
[8] J. Zhao and Q. Yang, Several solution methods for the split feasibility problem,
Inverse Problems 21 (2005), 1791-1799.
[9] H. K. Xu, A variable Krasnosel0ski˘ı-Mann algorithm and the multiple-set split
feasibility problem, Inverse Problems 22 (2006), 2021-2034.
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