论文标题
不受限制的道格拉斯 - 拉赫福德算法用于解决希尔伯特空间中的凸的可行性问题
Unrestricted Douglas-Rachford algorithms for solving convex feasibility problems in Hilbert space
论文作者
论文摘要
在这项工作中，我们着重于希尔伯特领域的凸出可行性问题（CFP）。 Douglas-Rachford（DR）算法是该领域中引起了很多兴趣的一种具体方法。该算法最初是在1956年推出的，用于求解固定和非平稳热方程。然后在1979年，狮子和Mercier调整了算法并扩展了算法，目的是解决CFP和更一般的问题，例如找到两个最大单调算子的总和。在过去的十年中，许多实施有关该算法的概念的发展发生了。我们引入了一种无限制的算法，该算法为此类概念提供了一个一般框架。使用有限数量的大量非专业运算符的不受限制的产品，我们将此框架应用于提供新的迭代方法，其中，\ textit {Interiarie}可以在我们的\ Unranded \ color color color dr算法的方案中使用的操作员交错。
In this work we focus on the convex feasibility problem (CFP) in Hilbert space. A specific method in this area that has gained a lot of interest in recent years is the Douglas-Rachford (DR) algorithm. This algorithm was originally introduced in 1956 for solving stationary and non-stationary heat equations. Then in 1979, Lions and Mercier adjusted and extended the algorithm with the aim of solving CFPs and even more general problems, such as finding zeros of the sum of two maximally monotone operators. Many developments which implement various concepts concerning this algorithm have occurred during the last decade. We introduce an unrestricted DR algorithm, which provides a general framework for such concepts. Using unrestricted products of a finite number of strongly nonexpansive operators, we apply this framework to provide new iterative methods, where, \textit{inter alia}, such operators may be interlaced between the operators used in the scheme of our \ unrestricted \color DR algorithm.
