标题： 一种用于锥体最小基数生成器的算法 显示英文标题

标题： An algorithm for minimum cardinality generators of cones

摘要： 本文提出了一种新颖的证明，表明对于任何凸锥，锥独立生成元的大小最多是最小基数生成元的两倍。 虽然这一结果在线性空间中已知，但我们通过将其分解为线性和尖锐成分，将其扩展到一般锥体。 我们的构造性方法导致了一个多项式时间算法，用于计算有限生成锥体的最小基数生成元，优于现有仅计算锥独立生成元的方法。 显示英文摘要

摘要： This paper presents a novel proof that for any convex cone, the size of conically independent generators is at most twice that of minimum cardinality generators. While this result is known for linear spaces, we extend it to general cones through a decomposition into linear and pointed components. Our constructive approach leads to a polynomial-time algorithm for computing minimum cardinality generators of finitely generated cones, improving upon existing methods that only compute conically independent generators.