Explicit solutions for interval semidefinite linear programs Original Research Article

We consider the special class of semidefinite linear programs image(IVP) maximize traceCX subject to Lnot precedes, equalsA(X)not precedes, equalsU, where C, X, L, U are symmetric matrices, A is an (onto) linear operator, and not precedes, equals denotes the Löwner (positive semidefinite) partial order. We present explicit representations for the general primal and dual optimal solutions. This extends the results for standard linear programming that appeared in Ben-Israel and Charnes [3]. This work is further motivated by the explicit solutions for a different class of semidefinite problems presented recently in Yang and Vanderbei [15].