Symmetrized separable convex programming

Abstract

The duality model for convex programming studied recently by E. L. Peterson is analyzed from the viewpoint of perturbational duality theory. Relationships with the traditional Lagrangian model for ordinary programming are explored in detail, with particular emphasis placed on the respective dual problems, Kuhn-Tucker vectors, and extremality conditions. The case of homogeneous constraints is discussed by way of illustration. The Slater existence criterion for optimal Lagrange multipliers in ordinary programming is sharpened for the case in which some of the functions are polyhedral. The analysis generally covers nonclosed functions on general spaces and includes refinements to exploit polyhedrality in the finite-dimensional case. Underlying the whole development are basic technical facts which are developed concerning the Fenchel conjugate and preconjugate of the indicator function of an epigraph set.