中心切片（中心路径的推广）
Central Swaths (A Generalization of the Central Path)
AI总结：
本文通过双曲锥的导数锥概念推广了中心路径，证明了导数锥固有的动力学总能生成通向最优性的路径，且高阶导数锥可能比中心路径更快收敛。
摘要：
我们提出了中心路径概念的一个自然推广——中心路径是凸优化内点法的核心。该推广通过“双曲锥”的“导数锥”实现，导数锥是对底层（双曲）锥约束（如非负象限、半正定矩阵锥等）的直接且数学上吸引人的松弛。我们证明了导数锥固有的动力学总能生成通向最优性的路径，而中心路径是导数锥为二次时的特例。更高阶的导数锥能更好地拟合底层锥约束，从而有望比中心路径更快地达到最优性。
英文摘要：
We develop a natural generalization to the notion of the central path -- a notion that lies at the heart of interior-point methods for convex optimization. The generalization is accomplished via the "derivative cones" of a "hyperbolicity cone," the derivatives being direct and mathematically-appealing relaxations of the underlying (hyperbolic) conic constraint, be it the non-negative orthant, the cone of positive semidefinite matrices, or other. We prove that a dynamics inherent to the derivative cones generates paths always leading to optimality, the central path arising from a special case in which the derivative cones are quadratic. Derivative cones of higher degree better fit the underlying conic constraint, raising the prospect that the paths they generate lead to optimality quicker than the central path.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
