korlátozáshalmaz

Korlátozáshalmaz is a mathematical concept primarily used in optimization theory, operations research, and systems analysis. It refers to a collection of constraints that limit the possible values of variables within a mathematical model or system. These constraints define the feasible region, or the set of all solutions that satisfy the specified limitations.

In the context of linear programming, a korlátozáshalmaz is formed by a finite set of linear inequalities or equations. The intersection of these inequalities delineates the feasible region, which is a convex polyhedron in many cases. The goal in such models is often to optimize an objective function within this feasible set.

The term originates from Hungarian, where "korlátozá" means "limitation" or "restriction," and "halmaz" means "set." As such, it emphasizes the notion of a set that encapsulates all limitations imposed on a system or problem.

Korlátozáshalmazs are critical in modeling real-world problems where resources, capacities, or other factors impose restrictions on possible solutions. For example, in logistics, constraints may include maximum load capacities, delivery deadlines, or budget limits. Understanding and analyzing the structure of such constraint sets helps in designing efficient algorithms to find optimal solutions or in performing sensitivity analysis.

In summary, a korlátozáshalmaz is a fundamental concept representing the set of all feasible solutions constrained by specific limitations. Its analysis forms the basis for solving constrained optimization problems across various scientific and engineering disciplines.