Global optimality conditions for nonconvex minimization problems with quadratic constraints

In this paper, some global optimality conditions for nonconvex minimization problems subject to quadratic inequality constraints are presented. Then some sufficient and necessary global optimality conditions for nonlinear programming problems with box constraints are derived. We also establish a sufficient global optimality condition for a nonconvex quadratic minimization problem with box constraints, which is expressed in a simple way in terms of the problem’s data. In addition, a sufficient and necessary global optimality condition for a class of nonconvex quadratic programming problems with box constraints is discussed. We also present some numerical examples to illustrate the significance of our optimality conditions.