miny

MinY is a term used to denote the smallest value of a quantity Y within a specified domain. In geometry, it often refers to the smallest y-coordinate among a set of points. In analysis and optimization, it represents the minimum value attained by a real-valued function Y = f(x) over a given domain D.

Notation for minY varies. It is commonly written as y_min = min { f(x) : x ∈ D } when the minimum is attained. If the minimum may not be achieved but a greatest lower bound exists, it is described using the infimum, y_min = inf { f(x) : x ∈ D }. In optimization, the point where the minimum occurs is called the argmin, the argument that minimizes the function.

Calculation methods depend on the context. For discrete data, minY is found by identifying the smallest y-value in the sample. For continuous functions, one typically finds critical points by setting the derivative to zero and checks boundary points to determine the actual minimum.

Examples illustrate the concept. A dataset with points (1,3), (2,5), (3,2) has minY = 2. For the function y = f(x) = x^2 + 1 on [-2, 2], the minimum value is y_min = 1, achieved at x = 0.

MinY is used across mathematics, statistics, data analysis, and optimization to describe extremal behavior of quantities and to compare datasets or models. Related concepts include maximum, infimum, supremum, and argmin.