The Method of Lagrange Multiplicators

This high confidence method is used when one or more equality constraints are imposed on the parameters of the process [3.61]. So, if our problem is to obtain the minimal value of function l (Pi,P2, Pl) the parameters requirement to verify the constraints fi(pi,P2, i = 1 g simultaneously, then the solution is obtained from the formulation of the following auxiliary function  

Function L(pj,p2,. ..pL, i, supports the same minimization as (Pi, P2, Pl) but here, the number of parameters is increased with, 2 which are called the Lagrange multiplicators. Then, the equation system that must be solved here is written as  

From Eq. (3.210) we can obtain one or more set(s) of values for pi,p2. Pl which give for function l (pi,P2, ---Pl) more extreme values. If we have various 

---