SIAM Journal on Optimization, Volume 31, Issue 1, Page 626-652, January 2021.
The split equality problem (SEP) seeks a pair of points $(x^{\ast },y^{\ast })\in (C,D)$ with the property that $Ax^{\ast }=By^{\ast }$, where $C,D$ are nonempty closed convex subsets of Hilbert spaces $\mathcal{H}_{1}$ and $% \mathcal{H}_{2}$, respectively, and $A:\mathcal{H}_{1}\rightarrow \mathcal{H}% _{3}$ and $B:\mathcal{H}_{2}\rightarrow \mathcal{H}_{3}$ are bounded linear operators, where $\mathcal{H}_{3}$ is another Hilbert space. The SEP can equivalently be converted to a split feasibility problem in the product space $\mathcal{H}_{1}\times \mathcal{H}_{2}$. Using this equivalence, we are able to provide a Landweber operator approach to studying the convergence of several iterative methods for finding a solution to the SEP. We also discuss the linear regularity of the Landweber operator associated with the SEP and linear convergence of the iterative methods.

中文翻译：

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分裂等式问题的Landweber算子方法

SIAM优化杂志，第31卷，第1期，第626-652页，2021年1月。
分裂相等问题（SEP）在（C，D）$中寻找一对点$（x ^ {\ ast}，y ^ {\ ast}）\ in（C，D）$，其属性为$ Ax ^ {\ ast} = By ^ {\ ast} $，其中$ C，D $分别是希尔伯特空间$ \ mathcal {H} _ {1} $和$％\ mathcal {H} _ {2} $和$ A的非空封闭凸子集：\ mathcal {H} _ {1} \ rightarrow \ mathcal {H}％_ {3} $和$ B：\ mathcal {H} _ {2} \ rightarrow \ mathcal {H} _ {3} $有界线性运算符，其中$ \ mathcal {H} _ {3} $是另一个希尔伯特空间。SEP可以等效地转换为产品空间$ \ mathcal {H} _ {1} \ times \ mathcal {H} _ {2} $中的分裂可行性问题。使用这种等效性，我们能够提供一种Landweber算子方法来研究几种迭代方法的收敛性，以找到SEP的解决方案。