Indicator of power convex and exponential transformations for solving nonlinear problems containing posynomial terms

Posynomial terms frequently appear in many nonlinear problems and are the core components of geometric and generalized geometric programming problems. The most popular method to treat nonconvex posynomial terms for obtaining global optimization is to convert nonconvex posynomial terms as convex underestimators using transformation techniques. Among the transformation techniques, exponential transformation (ET) and power convex transformation (PCT) can yield the tightest underestimators of posynomial terms. However, the current literature has rarely discussed which to select between ET and PCT. This study employs the definite integral with piecewise linear technique to calculate the error between the original posynomial and the corresponding ET/PCT underestimators. Lastly, this study aims to identify an indicator that can choose the appropriate transformation between ET and PCT and analyze the correctness of the proposed indicator for posynomial terms in nonlinear problems. The proposed indicator can efficiently solve nonlinear problems containing posynomial terms. Numerical examples are used to demonstrate the efficacy of the proposed indicator.