On subsidiary problems in geometric programming

When a dual-based procedure is used to solve a geometric programming problem, the presence of inactive constraints at the primal optimum reduces the amount of information available about the relationship between the optimal primal and dual vectors. In certain situations one must resort to solving one or more subsidiary problems to recover solution from the dual optimum. This paper reviews such situations and presents an alternative formulation of the dual as a generalized linear program, along with a column generation algorithm based on the same. The algorithm avoids subsidiary problems, and the formulation provides more information than the traditional dual when recovering the primal optimum.