论文标题
四个操作员通过线路搜索通过前向后卫算法分开
Four Operator Splitting via a Forward-Backward-Half-Forward Algorithm with Line Search
论文作者
论文摘要
在本文中，我们提供了一种分裂方法，用于在涉及四个操作员的真实希尔伯特空间中求解单调夹杂物：最大单调，单调 - lipschitzian，cocoercive和一个单调连续算子。所提出的方法利用了每个操作员的固有属性，从而通过线路搜索概括了前后后半方的前向前分裂和Tseng的算法。在每次迭代中，我们的算法通过使用一条线搜索来定义步骤大小，在该搜索中，单调 - 莱普齐斯和cocoercive oberator只需要一个激活。我们还得出了一种解决实际希尔伯特空间中非线性约束复合凸优化问题的方法。最后，我们在非线性约束最小二乘问题中实现算法，并将其性能与文献中的可用方法进行比较。
In this article we provide a splitting method for solving monotone inclusions in a real Hilbert space involving four operators: a maximally monotone, a monotone-Lipschitzian, a cocoercive, and a monotone-continuous operator. The proposed method takes advantage of the intrinsic properties of each operator, generalizing the forward-back-half forward splitting and the Tseng's algorithm with line-search. At each iteration, our algorithm defines the step-size by using a line search in which the monotone-Lipschitzian and the cocoercive operators need only one activation. We also derive a method for solving non-linearly constrained composite convex optimization problems in real Hilbert spaces. Finally, we implement our algorithm in a non-linearly constrained least-square problem, and we compare its performance with available methods in the literature.
