Duality in infinite dimensional linear programming

Abstract

We consider the class of linear programs with infinitely many variables and constraints having the property that every constraint contains at most finitely many variables while every variable appears in at most finitely many constraints. Examples include production planning and equipment replacement over an infinite horizon. We form the natural dual linear programming problem and prove strong duality under a transversality condition that dual prices are asymptotically zero. That is, we show, under this transversality condition, that optimal solutions are attained in both primal and dual problems and their optimal values are equal. The transversality condition, and hence strong duality, is established for an infinite horizon production planning problem.