Global optimality conditions for nonlinear programming problems with linear equality constraints

Some necessary global optimality conditions and sufficient global optimality conditions for nonconvex minimization problems with a quadratic inequality constraint and a linear equality constraint are derived. in particular,global optimality conditions for nonconvex minimization over a quadratic inequality constraint which extend some known global optimality conditions in the existing literature are presented. some numerical examples are also given to illustrate that a global minimizer satisfies the necessary global optimality conditions but a local minimizer which is not global may fail to satisfy them. © 2014 guoquan li and yan wang.