V2EX dual variable

Dual Variable

定义 Definition

对偶变量:在线性规划、凸优化等问题的对偶问题(dual problem)中出现的变量,常用于刻画原问题约束的“影子价格/边际价值”,并与拉格朗日乘子(Lagrange multiplier)密切相关。(在不同语境下也可指一般“对偶空间”中的变量,但优化中最常见。)

发音 Pronunciation (IPA)

/dul vribl/(亦常见 /dul vribl/)

例句 Examples

The dual variable tells us how tight the constraint is.
对偶变量告诉我们这个约束有多“紧”(对目标的限制有多强)。

In constrained optimization, interpreting each dual variable as a shadow price can explain how the optimal objective value changes when we slightly relax a constraint.
在约束优化中,把每个对偶变量解释为影子价格,有助于说明当我们稍微放宽某个约束时,最优目标值会如何变化。

词源 Etymology

dual 来自拉丁语 dualis(“二、成对的”),表示“对偶/成对”的概念;variable 来自拉丁语 variabilis(“可变化的”)。合起来 dual variable 指“对偶(另一侧)问题中的变量”,与“原(primal)问题”相对应。

相关词 Related Words

文学与经典著作 Literary Works

  • Convex Optimization Stephen Boyd & Lieven Vandenberghe(凸优化经典教材,系统使用“dual variables/拉格朗日乘子”)
  • Linear Programming Vasek Chvátal(线性规划教材,讨论对偶与对偶变量)
  • Introduction to Operations Research Hillier & Lieberman(运筹学教材,影子价格与对偶变量的解释常见)
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