Constrained Gauss-Newton Method for Regression of Binary VLE Data

3 Constrained Gauss-Newton Method for Regression of Binary VLE Data 

As we mentioned earlier, this is not a typical constrained minimization problem although the development of the solution method is very similar to the material presented in Chapter 9. If we assume that an estimate k(J) is available at the j,h iteration, a better estimate, k(J+l), of the parameter vector is obtained as follows. 

Linearization of the residual vector e = [/ f/ — // f,v, /nfj -/nf2V] around kw at the irt data point yields 

Equation 14.32a is solved for Ak and the result is substituted in Equation 14.32b which is then solved for co to yield 

Substituting the above expression for the Lagrange multiplier into Equation 14.32a we arrive at the following linear equation for Ak0+1), 

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