Maximized

Maximized is the past participle of maximize, and it is used to indicate that something has been increased to its greatest possible extent within given constraints. In everyday language, a resource or value that is maximized is as large or as high as allowed by the situation.

In mathematics and related fields, to maximize a function f over a domain D is to determine its largest value, the maximum, together with the input(s) that achieve it (the arg max). A maximum can be global (the largest value on the entire domain) or local (the largest within a neighborhood). Methods include calculus (finding critical points by setting derivatives to zero and applying second-order tests), convex analysis, and constrained optimization techniques such as Lagrange multipliers and linear programming.

In computing and user interfaces, "maximized" often describes a window state where the interface element fills the available screen space, typically expanding to the full display and hiding other decorations until restored.

In statistics, the term appears in estimation methods such as maximum likelihood estimation, where parameters are chosen to maximize a likelihood function given observed data.