I have the analytical first and second derivatives of a (multidimensional) lagrangian ( l = f - λh). X is the vector of variables of the objective function and λ is the single lagrange multiplier. where f=f(X) is the nonlinear objective function, h is the nonlinear (equality) constraint (i.e. h(X) - ρ = 0 at optimized solution). I'm generally confused about how to solve this (i've read about the "Lagrange-Newton (SOLVER) method" but don't really understand it. How do I update X and λ? Please try to be as specific as possible. Thanks.