An Efficient Global Approach for Posynomial Geometric Programming Problems

Aposynomial geometric programming problem is composed of a posynomial being minimized in the objective function subject to posynomial constraints. This study proposes an efficient method to solve a posynomial geometric program with separable functions. Power transformations and exponential transformations are utilized to convexify and underestimate posynomial terms. The inverse transformation functions of decision variables generated in the convexification process are approximated by superior piecewise linear functions. The original program therefore can be converted into a convex mixed‐integer nonlinear program solvable to obtain a global optimum. Several numerical experiments are presented to investigate the impact of different convexification strategies on the obtained approximate solution and to demonstrate the advantages of the proposed method in terms of both computational efficiency and solution quality.