  We study nonconvex quadratic problems (QPs) with quadratic separable
constraints, where these constraints can be defined both as inequalities or
equalities. We derive sufficient conditions for these types of problems to
present the S-property, which ultimately guarantees strong duality between the
primal and dual problems of the QP. We study the existence of solutions and
propose a novel distributed algorithm to solve the problem optimally when the
S-property is satisfied. Finally, we illustrate our theoretical results proving
that the robust least squares problem with multiple constraints has the strong
duality property.
