The solution of a constrained optimization problem at which one or more constraints are binding. Also referred to as constrained maximum (minimum) when optimization involves maximizing (minimizing) the objective function. Assume f  (x) is to be maximized subject to the constraints g_i(x) ≥ 0, i = 1,…, m, where x = (x₁,…, x_n). Then the maximum occurs at a saddle point of the Lagrangian function

with L maximized for each x_i and minimized for λ‎_i. The optimum is constrained if, at the saddle point, at least one of the constraints holds as an equality. Examples of constrained optima are the maximization of utility subject to a budget constraint for a consumer who is never satiated, and the minimization of cost subject to a production constraint for a firm employing factors of production with strictly positive prices.