Semidefinite linear programming (SDP) is a generalization of LP where the non-negativity constraints are replaced by a semidefiniteness constraint on the matrix variables. There are many applications, e.g. in systems and control theory and in combinatorial optimization. However, the Lagrangian dual for SDP can have a duality gap. We discuss the relationships among various duals and give a unified treatment for strong duality in semidefinite programming. These duals guarantee strong duality, i.e. a zero duality gap and dual attainment. This paper is motivated by the recent paper by Ramana where one of these duals is introduced.
CORR 95-12, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, June 1995.