A point at which a function of several variables is at a maximum for movement in some directions and a minimum for movement in the remaining directions. Assume f(x) is to be maximized subject to g(x) ≥ 0, where x = (x1,…, xn). Then the maximum occurs at a saddle point of the Lagrangian function L ≡ f(x) + λg(x), with L maximized for each xi and minimized for λ.