Conic Linear Programming Duals for Classes of Quadratic Semi-Infinite Programs with Applications

In this paper, we first present strong conic linear programming duals for convex quadratic semi-infinite problems with linear constraints and geometric index sets. The obtained results show that the optimal values of a convex quadratic semi-infinite problem with convex compact sets and its associated conic linear programming dual problem are equal with the solution attainment of the dual program. We then prove that the conic linear programming dual is equivalently reformulated as a second-order cone programming problem whenever the index sets are ellipsoids, balls, cross-polytopes or boxes. As an application, we show that a class of separable fractional quadratic semi-infinite programs also admits second-order cone programming duality under ellipsoidal index sets.