In this paper, we study a semi-definite and semi-infinite programming problem (SDSIP) with equality constraints. We establish that a uniform duality between a homogeneous (SDSIP) problem and its Lagrangian-type dual problem is equivalent to the closedness condition of certain cone. A corresponding result for a nonhomogeneous (SDSIP) problem is also obtained by transforming it into an equivalent homogeneous (SDSIP) problem.
- Semi-definite program
- Semi-infinite program