optimum

Optimum refers to the most favorable condition, level, or outcome for a given objective. As a noun, it denotes the best available state; as an adjective, it describes the best possible condition for a specific situation. The term is from Latin optimus, meaning "best." While "optimal" is a common adjective in many fields, "optimum" is widely used in engineering and formal writing to emphasize the best feasible point.

In mathematics and related disciplines, an optimum is a point at which an objective function attains its best value. For maximization problems, the optimum is the maximum value; for minimization, the minimum. Optima may be global, occurring over the entire feasible region, or local, being the best within a neighborhood. When constraints limit the feasible set, the best feasible solution is the constrained optimum.

Applications span science, engineering, economics, and operations research. Examples include the optimum temperature for a chemical reaction, the optimum speed of a mechanism, or the optimum portfolio mix. In economics, the Pareto optimum (or Pareto efficiency) describes a state where no one can be made better off without harming another.

See also optimization, optimality, and related concepts. The term remains common in technical contexts, while everyday usage often employs "optimal" as the preferred adjective, with "optimum" used especially to stress the best feasible point under stated conditions.