| # Digital Circuit Design: GP Model Circuit Design > Back | GP Model | Next Generalized posynomial model Explicit posynomial model ## Generalized Posynomial Representation We now consider the problem of choosing the scale factors to minimize the total delay, subject to an area constraint. where is an upper bound on the area of each gate. Since is a maximum of function of , itself a posynomial in , we can express the total delay as a posynomial in . Hence the above is a GP. ## Explicit Posynomial Representation Let us form the GP in a more explicit way, using the intermediate variables , which we encountered in our definition of the delay. The basic idea is to replace the equality defining these intermediate variables, e.g. by inequalities: It turns out we ‘‘loose nothing’’ in this process; that is, at optimum, equality holds. Mor generally, we replacing the constraint by a relaxed version: The above can be written: We obtain an explicit representation of the previous GP: The above is also a GP. At the expense of adding new variables and also adding constraints, we have obtained a sparser problem.