论文标题
用有限的多面体投影替换有限生成的凸锥的投影
Replacing projection on finitely generated convex cones with projection on bounded polytopes
论文作者
论文摘要
本文致力于由有限的发电机组产生的多面体凸锥的总体投影问题。该问题被重新注射到通过简单的原始锥体截断获得的多层物体中。然后，只需在相同的有限多层上使用两个密切相关的投影来解决它。该方法的计算性能是由关键工具的效率来解决的，该工具的效率是解决给定有限点的凸壳中找到最小规范元素的基本问题。在我们的数值实验中，我们将其用于此目的，用于矩阵矢量计算的开源系统中实现的专门有限算法八度。该算法实际上对发电机数量及其尺寸之间的比例无动于衷，并且在超过八度的数量超过原始问题的维度时，主动集变体的通用二次二次编程算法大大胜过了一个通用的二次编程算法。
This paper is devoted to the general problem of projection onto a polyhedral convex cone generated by a finite set of generators.This problem is reformulated into projection onto the polytope obtained by simple truncation of the original cone. Then it can be solved with just two closely related projections onto the same bounded polytope. This approach's computational performance is conditioned by the crucial tool's efficiency for solving the fundamental problem of finding the least norm element in a convex hull of a given finite set of points. In our numerical experiments, we used for this purpose the specialized finite algorithm implemented in the open-source system for matrix-vector calculations octave. This algorithm is practically indifferent to the proportions between the number of generators and their dimensionality and significantly outperformed a general-purpose quadratic programming algorithm of the active-set variety built into octave when the number of points exceeds the dimensionality of the original problem.
