TeXipedia

min

Represents the minimum value or minimization operation in mathematical expressions and optimization problems.

Overview

Essential in optimization theory, computer science, and mathematical analysis for finding the smallest value in a set or expressing minimization objectives.

  • Commonly used in linear programming and algorithmic complexity notation
  • Appears frequently in constraint optimization problems
  • Often paired with subscripts to specify the variable or domain of minimization
  • Distinguished from regular text 'min' by proper mathematical spacing and formatting

Examples

Finding the minimum value in a set of numbers.

min⁡{3,7,2,9,4}=2\min\{3, 7, 2, 9, 4\} = 2 
\min\{3, 7, 2, 9, 4\} = 2

Optimization problem showing minimum of a quadratic function.

min⁡x∈R(x2+2x+1)\min_{x \in \mathbb{R}} (x^2 + 2x + 1) 
\min_{x \in \mathbb{R}} (x^2 + 2x + 1)

Minimum distance between two points in a metric space.

d(A,B)=min⁡{∣x−y∣:x∈A,y∈B}d(A,B) = \min\{|x-y| : x \in A, y \in B\} 
d(A,B) = \min\{|x-y| : x \in A, y \in B\}