Abstract

Many problems, for example, problems on the properties of the reachability set of a linear control system, are reduced to finding the projection of zero onto some convex compact subset in a finite-dimensional Euclidean space. This set is given by its support function. In this paper, we discuss some minimum sufficient conditions that must be imposed on a convex compact set so that the gradient projection method for solving the problem of finding the projection of zero onto this set converges with a linear rate. An example is used to illustrate the importance of such conditions.

中文翻译：

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求点在凸紧集上的度量投影的算法线性收敛的充分条件

摘要

许多问题，例如线性控制系统可达性集的性质问题，都被简化为寻找零在有限维欧几里德空间中某个凸紧子集上的投影。该集合由其支持函数给出。在本文中，我们讨论了一些必须施加在凸紧集上的最小充分条件，以便解决寻找零在该集上的投影问题的梯度投影方法以线性速率收敛。我们用一个例子来说明这些条件的重要性。