maximiser

Maximiser is a noun referring to a person or thing that increases something to its maximum level, or to an entity that chooses options to maximise a specified criterion. In British English, the spelling maximiser is common; American English usually uses maximizer. The term is used across mathematics, economics, computer science, and everyday language to describe an agent or tool that seeks the highest possible value of a target function.

In mathematics and optimization, the maximiser of a function f defined on a domain D is an element x* in D such that f(x*) ≥ f(x) for all x in D. When the equality holds at multiple points, one speaks of the set of maximisers. The problem of finding an input that achieves the maximum is called a maximization problem, and an input that yields the maximum is often written as the arg max: x* = arg max_x f(x). An algorithm that performs this search is called an optimizer or maximiser.

In economics and decision theory, a rational agent is modeled as a maximiser of a utility or profit function subject to constraints. In computer science and statistics, maximisers appear in optimization algorithms, machine learning model fitting by maximum likelihood, and in discrete optimization.

The term is often used without geographic distinction in general writing, but care should be taken to follow local spelling conventions. See also: maximum, maximum likelihood, argmax, optimization, optimizer.