A global interior point method for nonconvex geometric programming

The strategy presented in this paper differs significantly from existing approaches as we formulate the problem as a standard optimization problem of difference of convex functions. We have developed the necessary and sufficient conditions for global solutions in this standard form. The main challenge in the standard form arises from a constraint of the form g(t)≥1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g(t) \ge 1$$\end{document}, where g is a convex function. We utilize the classical inequality between the weighted arithmetic and harmonic means to overcome this challenge. This enables us to express the optimality conditions as a convex geometric programming problem and employ a predictor-corrector primal-dual interior point method for its solution, with weights updated during the predictor phase. The interior point method solves the dual problem of geometric programming and obtains the primal solution through exponential transformation. We have implemented the algorithm in Fortran 90 and validated it using a set of test problems from the literature. The proposed method successfully solved all the test problems, and the computational results are presented alongside the tested problems and the corresponding solutions found.