The effects of combining rules on the parameters A Ii,Jj , B Ii,Jj , and C Ii,Jj can also be enforced through the derivatives of the merit function by applying the chain rule of differentiation. For instance, if the parameter p k ′ depends on the parameter pk through a combining rule relationship (i.e., p k ′ (p k )), then the derivatives of pk can be modified to include this additional dependence through Equation ( ).