Convex relaxation for solving posynomial programs

摘要

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) X_2~(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 y_j = x_j~(-β_j) By specifying β_j carefully, we can find a tighter underestimation than the current methods.