Global optimality of quadratic minimization over symmetric polytopes

In this article, we establish necessary as well as sufficient conditions for a feasible point to be a global minimizer of a quadratic function over a symmetric polytope. We also show that the necessary condition becomes necessary and sufficient for global optimality in the special case where the matrices are involved diagonal matrices. Sufficient conditions are obtained by way of simple quadratic underestimation. Examples are discussed to illustrate the optimality conditions.