Convex relaxation for solving posynomial programs

Abstract

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)(alpha 1)x(2)(alpha 2) ... x(n)(alpha n), 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 beta(j), for all alpha(j) > 0, such that y(j) = x(j)(-beta j). By specifying beta(j) carefully, we can find a tighter underestimation than the current methods.