V2EX interior-point

Interior-point

释义 Definition

内点(法):在线性规划、凸优化等问题中,一类从可行域内部出发并沿着“中心路径(central path)”迭代逼近最优解的算法家族,常用于大规模优化。也可作形容词用,指“内点法的/采用内点法的”。(在其他语境中 interior 也有“内部的”,point 有“点/观点”等常见义。)

发音 Pronunciation (IPA)

/ntrir pnt/

例句 Examples

We solved the optimization problem with an interior-point method.
我们用内点法解决了这个优化问题。

For large sparse constraints, interior-point algorithms often converge reliably and scale better than the simplex method.
对于大型稀疏约束问题,内点算法往往收敛更稳定,并且比单纯形法更易扩展到更大规模。

词源 Etymology

该词由 interior(内部的) + point(点) 组合而成。内点法之所以得名,是因为它的迭代点通常保持在可行域“内部”,并通过障碍函数(barrier)等思想避免直接落到边界上,从而逐步逼近最优解所在的边界/顶点。

相关词 Related Words

文学与著作 Literary Works

  • Stephen Boyd & Lieven Vandenberghe, Convex Optimization(讨论内点法与障碍方法的经典教材)
  • Jorge Nocedal & Stephen J. Wright, Numerical Optimization(系统介绍内点法、原始-对偶方法等)
  • Yurii Nesterov & Arkadii Nemirovskii, Interior-Point Polynomial Algorithms in Convex Programming(内点法理论的重要专著)
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