In optimization, a problem is defined using an objective function to minimize or maximize, and a set of constraints that should be respected. The active set is the set of constraints that are active at the solution (that is saturated, for example x <= 300 is active for x = 300 and not active for x = 250).

The active set is particularly important in optimization theory as it determines which constraints will influence the final result of optimization. For example, in solving the linear programming problem, the active set gives the hyperplanes that intersect at the solution point. In quadratic programming, as the solution is not mandatorily on one of the edges of the bounding polygon, an estimation of the active set gives us a subset of inequalities to watch while searching the solution, which reduces the complexity of the search.