Global quadratic minimization over bivalent constraints: Necessary and sufficient global optimality condition

In this paper, we establish global optimality conditions for quadratic optimiza-tion problems with quadratic equality and bivalent constraints. We first present a necessary and sufficient condition for a global minimizer of quadratic optimiza-tion problems with quadratic equality and bivalent constraints. Then, we examine situations where this optimality condition is equivalent to checking the positive semidefiniteness of a related matrix, and so, can be verified in polynomial time by using elementary eigenvalues decomposition techniques. As a consequence, we also present simple sufficient global optimality conditions, which can be verified by solv-ing a linear matrix inequality problem, extending several known sufficient optimality conditions in the existing literature