V2EX slack variable

Slack Variable

释义 Definition

Slack variable松弛变量。在线性规划等优化问题中,为了把“不等式约束(≤ 或 ≥)”改写成“等式约束(=)”而引入的非负辅助变量,用来表示约束的“剩余量/富余量”。

发音 Pronunciation (IPA)

/slk vrib()l/

例句 Examples

A slack variable turns a “≤” constraint into an equality.
松弛变量把“≤”约束转换为等式约束。

In the simplex method, adding slack variables allows the problem to be written in standard form so that a basic feasible solution can be found.
在单纯形法中,引入松弛变量可以把问题写成标准形式,从而找到一个基本可行解。

词源 Etymology

slack 本义有“松弛的、余量的”之意,在约束条件里对应“未用尽的容量/剩余”;variable 表示“变量”。合起来就是“表示约束余量的变量”,因此译作“松弛变量”。

相关词 Related Words

文学与著作 Literary & Notable Works

  • George B. Dantzig, Linear Programming and Extensions(线性规划经典著作,讨论标准形式与松弛变量)
  • Dimitris Bertsimas & John N. Tsitsiklis, Introduction to Linear Optimization(教材中用松弛变量将不等式转为等式)
  • Stephen Boyd & Lieven Vandenberghe, Convex Optimization(涉及将约束改写、引入辅助变量的相关表述)
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