What is Karush–Kuhn–Tucker conditions?

The Karush–Kuhn–Tucker conditions at $(x, \lambda, \nu)$ are primal feasibility, dual feasibility ($\lambda \ge 0$), complementary slackness ($\lambda_ig_i(x) = 0$) and stationarity, $\nabla f(x) + \sum_i\lambda_i\nabla g_i(x) + A^\top\nu = 0$ (Karush, 1939; Kuhn and Tucker, 1951).