This article is concerned with the problem of approximating a not necessarily bounded spectrahedral shadow, a certain convex set, by polyhedra. By identifying the set with its homogenization, the problem is reduced to the approximation of a closed convex cone. We introduce the notion of homogeneous \(\delta \)-approximation of a convex set and show that it defines a meaningful concept in the sense that approximations converge to the original set if the approximation error \(\delta \) diminishes. Moreover, we show that a homogeneous \(\delta \)-approximation of the polar of a convex set is immediately available from an approximation of the set itself under mild conditions. Finally, we present an algorithm for the computation of homogeneous \(\delta \)-approximations of spectrahedral shadows and demonstrate it on examples.

本文涉及用多面体逼近不一定有界的谱面阴影（某个凸集）的问题。通过识别集合的同质化，问题被简化为封闭凸锥体的近似。我们引入了凸集的齐次\(\delta \)逼近的概念，并表明它定义了一个有意义的概念，即如果逼近误差\(\delta \)减小，则近似收敛到原始集。此外，我们表明，在温和条件下，凸集的极坐标的齐次\(\delta \)近似可以立即从该集合本身的近似中获得。最后，我们提出了一种计算谱面阴影的齐次 δ近似的算法，并通过示例进行了演示。