On complementary polar conical sets

Abstract

Abstract : Tucker has formulated the Duality Theorem of Linear Programming in terms of orthogonality properties of a pair of complementary orthogonal linear manifolds with respect to the positive orthant. This theorem is generalized by substituting complementary polar conical sets for complementary orthogonal linear manifolds, and proved under simple stability assumptions. Equivalence to Feuchel's Duality Theorem for conjugate convex functions is established. There are strong parallelisms to work by Kretschmer. (Author)