Mulighetsområdet

Mulighetsområdet is a Norwegian term that translates roughly to the set of possibilities or the space of possibilities. In mathematics, optimization, statistics, and decision analysis it refers to the collection of values or configurations that satisfy a given set of constraints. It is commonly called the feasible set or feasible region in English. The mulighetsområdet contains all points that meet all the specified conditions, such as equations and inequalities, that define a problem. The objective function is then optimized over this region; properties of the region, such as convexity or discreteness, influence the choice of solution methods and the nature of the optimum.

In a typical optimization problem, the mulighetsområdet is defined by constraints. For example, in a linear programming problem with the goal of maximizing c^T x subject to Ax ≤ b and x ≥ 0, the mulighetsområdet is the set of all x in R^n satisfying Ax ≤ b and x ≥ 0. If the constraints are linear, the region is a convex polyhedron; if there are only bounds, it may be a simple hyper-rectangle. When integrality constraints are present, the mulighetsområdet becomes a discrete set of feasible points.

Beyond mathematics, the term is used in statistics, where it can denote the parameter space consistent with the model and data, and in policy or design contexts to describe the range of permissible options or actions. The mulighetsområdet thus serves to separate the space of possible choices from the goal of selecting the best or most appropriate option within that space.