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
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Studies in Advanced Mathematics, vol. 28, Cambridge University Press, 1990.
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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.
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feasibility problem, Inverse Problems 22 (2006), 2021-2034.