论文标题
与重新扰动重新扰动的卓越方法，用于分裂最小化问题，并应用放疗治疗计划
The superiorization method with restarted perturbations for split minimization problems with an application to radiotherapy treatment planning
论文作者
论文摘要
在本文中，我们研究了分裂最小化问题，该问题包括两个约束最小化问题，这两个单独的空间是通过线性操作员连接的两个单独的空间，该空间将一个空间映射到另一个空间。为了处理此类问题的数据，我们开发了一种出色的方法，该方法可以达到可行的点，而（不一定是最小）的目标函数值。优越的方法是基于通过另一个过程所决定的步骤扰动一个过程的迭代来交织两个单独且独立的迭代过程的迭代步骤。我们在开发的方法中包括两个新元素。第一个是在优越算法中重新启动扰动的许可，这导致了显着的加速并提高了计算效率。第二个要素是独立优化子向量的能力。如下所示，这满足了现实世界应用的需求，这在强度调节的放射治疗治疗计划中存在问题。
In this paper we study the split minimization problem that consists of two constrained minimization problems in two separate spaces that are connected via a linear operator that maps one space into the other. To handle the data of such a problem we develop a superiorization approach that can reach a feasible point with reduced (not necessarily minimal) objective function values. The superiorization methodology is based on interlacing the iterative steps of two separate and independent iterative processes by perturbing the iterates of one process according to the steps dictated by the other process. We include in our developed method two novel elements. The first one is the permission to restart the perturbations in the superiorized algorithm which results in a significant acceleration and increases the computational efficiency. The second element is the ability to independently superiorize subvectors. This caters to the needs of real-world applications, as demonstrated here for a problem in intensity-modulated radiation therapy treatment planning.
