minimumpunt

Minimumpunt is a term that some writers use to refer to a point where a real-valued function attains its minimum value on a specified domain. In standard terminology, this point is called a minimum point or minimizer, and the corresponding function value is the minimum. The minimum can be global (the smallest value over the entire domain) or local (the smallest value within a neighborhood).

In single-variable calculus, a local minimum occurs at a point x* where f'(x*) = 0 and f''(x*) > 0, or at endpoints. In multivariate settings, a differentiable local minimum occurs where the gradient vanishes and the Hessian is positive semidefinite; for convex functions, any local minimum is global.

Finding minimumpunts involves optimization methods: gradient descent, Newton's method, subgradient methods for non-differentiable cases; global methods for non-convex problems include restarts, heuristic algorithms, or convex relaxations.

Relation to terminology: The minimumpunt corresponds to the minimizer (argmin) of a function; the minimum value is min f(x). Applications include machine learning loss minimization, operations research, economics, physics, and engineering.