In mathematical optimization, the active-set method is an algorithm used to identify the active constraints in a set of inequality constraints. The active constraints are then expressed as equality constraints, thereby transforming an inequality-constrained problem into a simpler equality-constrained subproblem. An optimization problem is defined using an objective function to minimize or maximize, and a set of constraints that define the feasible region, that is, the set of all x to search for the optimal solution. Given a point in the feasible region, a constraint