Lagrangian

For \min f_0(x) s.t. f_i(x)\le0 and h_j(x)=0, the Lagrangian is L(x,\lambda,\mu) = f_0(x) + \sum_i \lambda_i f_i(x) + \sum_j \mu_j h_j(x), folding every constraint into the objective via a Lagrange multiplier (\lambda_i\ge0 for each inequality, \mu_j unrestricted in sign for each equality). Setting the Lagrangian's gradient (with respect to x) to zero is the stationarity condition at the heart of both Lagrange-multiplier problems and the KKT conditions.