Convex underestimation techniques for nonlinear functions are an essential part of global optimization. These techniques usually involve the addition of new variables and constraints. In the case of posynomial functions x 1 α1 x2 α2 ⋯ x n αn logarithmic transformations (Maranas and Floudas, Comput. Chem. Eng. 21:351-370, 1997) are typically used. This study develops an effective method for finding a tight relaxation of a posynomial function by introducing variables y j and positive parameters β j, for all α j > 0, such that yj =xj -βj. By specifying β j carefully, we can find a tighter underestimation than the current methods.
- Convex underestimation
- Posynomial functions