On a classification scheme for geometric programming and complementarity theorems†^†

This report was prepared as part of the activities of Management Sciences Research Group, Carnegie-Mellon University and supported in part by National Science Foundation Grant GK-31833

Abstract

A classification theorem is given stating that out of 18 duality states between a pair of dual geometric programs only 7 are possible. The impossible states are proved by using the duality results of Duffin-Peterson-Zener [9] and two properties associated with a subconsistent primal: (1) if the subinfimum is 0, then the dual is inconsistent and (2) if the subinfimum is + α, then the dual is consistent and unbounded. New complementarity theorems are also given between a given term of a posynomial and the associated dual variable. These results apply to subconsistent programs thereby generalizing results of Avriel-Williams [1]

This report was prepared as part of the activities of Management Sciences Research Group, Carnegie-Mellon University and supported in part by National Science Foundation Grant GK-31833

This report was prepared as part of the activities of Management Sciences Research Group, Carnegie-Mellon University and supported in part by National Science Foundation Grant GK-31833

Notes

This report was prepared as part of the activities of Management Sciences Research Group, Carnegie-Mellon University and supported in part by National Science Foundation Grant GK-31833