Optimization of a Water Tank: Convex Form of the GPThe 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: |