V2EX interior-point method

Interior-Point Method

Definition / 释义

(数学优化)内点法:一类用于求解线性规划、二次规划与更一般凸优化问题的数值算法。其核心思想是在可行域的内部沿着由障碍函数(barrier)或原始-对偶条件引导的路径迭代逼近最优解,而不是在边界上“走角点”。

Pronunciation / 发音

/ntrir pnt mθd/

Examples / 例句

Interior-point methods can solve large linear programs efficiently.
内点法可以高效求解大规模线性规划问题。

In practice, a primal-dual interior-point method often converges in a small number of iterations even for difficult convex problems.
在实践中,即使面对较困难的凸优化问题,原始-对偶内点法也常常在较少迭代次数内收敛。

Etymology / 词源

“Interior-point”字面意思是“内部点”:强调迭代点保持在可行域内部;“method”表示方法/算法。该术语在优化领域广泛流行,尤其与20世纪80年代线性规划的突破性进展相关(如Karmarkar提出的多项式时间算法及随后发展的原始-对偶内点框架),使“内点法”成为与“单纯形法(simplex method)”并列的重要路线。

Related Words / 相关词

Literary Works / 文学作品

  • Stephen J. Wright, Primal-Dual Interior-Point Methods
  • Jorge Nocedal & Stephen J. Wright, Numerical Optimization
  • Stephen Boyd & Lieven Vandenberghe, Convex Optimization
  • Robert J. Vanderbei, Linear Programming: Foundations and Extensions
  • N. Karmarkar, “A New Polynomial-Time Algorithm for Linear Programming” (1984)
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