A review of duality theory for linear programming over topological vector spaces

In this paper duality theory for infinite dimensional linear programs is discussed in a topological vector space setting. Infinite dimensional linear programs occur in many different areas and the duality theory of such problems has been discussed by a number of authors. However, the results are scattered in the literature and are proved in a variety of different settings. The purpose of this paper is to bring together the main results on this subject and to present them in a unified setting and notation with some new simpler proofs.