Geometric programming problems with negative degrees of difficulty

Abstract This paper proposes two methods to solve posynomial geometric programs with negative degrees of difficulty of lower integral values. Such a case arises when a primal program has a number of variables equal or slightly greater than the number of terms. In this specific case the normality and the orthogonality conditions of the dual geometric program give a system of linear equations, where the number of linear equations is greater than the number of dual variables. No general solution vector exists for this system of linear equations. Either the least square or linear programming method can be applied to get an approximate solution vector for this system. Then the optimum value of the dual objective function can be obtained from the approximate solution vector.