Consistency, Superconsistency, and Dual Degeneracy in Posynomial Geometric Programming

This paper gives a method by which any consistent geometric programming problem may be reduced to a superconsistent or unconstrained geometric programming problem. We show that a consistent geometric programming problem is not superconsistent if and only if the dual geometric programming problem has an unbounded optimal solution set or an unattained supremum. Reduction of the dual to canonical form, i.e., reduction to an equivalent problem with a bounded optimal solution set, is shown to be dual to the reduction of a consistent primal program to an equivalent superconsistent program.