| # Optimization of a Water Tank: Convex Form of the GP GP > Posynomials | Standard Forms > Example: Water Tank Optimization | Applications The GP described here for the optimization of the shape of a water tank is Let us define the new variables: The objective function is transformed into Taking logarithms, the new objective function is where denotes the (convex) log-sum-exp function. The constraints all involve monomials, so they will translate into linear or affine constraints. For example, the aspect ratio constraint on : is equivalent to which, after taking logarithms, becomes the affine constraint: Thus, the original GP takes the standard convex form:
| The water tank optimization problem in convex form, corresponding to the values The design constraints of the problem are pictured as a forbidden region, in white. We observe that the cost function in this formulation is convex, contrary to that of the original problem.