Global optimization of a quadratic functional with quadratic equality constraints (Q1333357)

The authors study the constrained optimization problem \(\min x^T Qx\), subject to \(x^T Rx= 1\), \(x^T Sx= 1\), where the matrices \(Q\), \(R\), \(S\in R^{n\times n}\), \(R\) is positive definite and \(S\) is positive semidefinite. They develop a necessary and sufficient condition for a local solution of the minimization problem to be a global one.