Optimalet

Optimalet is the definite form of the adjective optimal used in Danish and Norwegian to refer to the optimum value or the best feasible solution in an optimization problem. In English, the term optimum or the word optimum is more common, but Scandinavian texts sometimes use optimalet when the noun form “the optimum” is needed.

In a mathematical optimization context, optimalet denotes a point x* in the decision variable space that yields the best value of an objective function under given constraints. If the problem has a unique best value, the optimum is unique; otherwise there may be multiple optima. The term global optimum (globalt optimum) refers to the best value over all feasible points, while a local optimum (lokalt optimum) is best in a neighborhood.

Common methods to identify optimalet include linear programming and integer programming for discrete decisions, convex optimization for smooth problems, and various algorithms such as the simplex method, interior-point methods, branch-and-bound, and dynamic programming.

The concept appears across disciplines, including operations research, economics, engineering, and computer science, wherever there is a need to maximize or minimize a measurable objective subject to constraints.

Etymology: optimalet derives from the adjective optimal, which itself traces to Latin optimum. In Danish and Norwegian, the suffix -et marks the definite neuter form used when referring to “the optimum.”

See also: optimum, optimization, optimality, global optimum, local optimum.