EXPLICIT SOLUTIONS FOR INTERVAL SEMIDEFINITE LINEAR-PROGRAMS

We consider the special class of semidefinite linear programs (IVP) ma ximize trace CX subject to L less than or equal to A(X) less than or e qual to U, where C, X, L, U are symmetric matrices, A is an (onto) lin ear operator, and less than or equal to denotes the Lowner (positive s emidefinite) partial order. We present explicit representations for th e general primal and dual optimal solutions. This extends the results for standard linear programming that appeared in Ben-Israel and Charne s [3]. This work is further motivated by the explicit solutions for a different class of semidefinite problems presented recently in Yang an d Vanderbei [15].