SECOND ORDER OPTIMALITY CONDITIONS AND REFORMULATIONS FOR NONCONVEX QUADRATICALLY CONSTRAINED QUADRATIC PROGRAMMING PROBLEMS

In this paper, we present an optimality condition which could determine whether a given KKT solution is globally optimal. This condition is equivalent to determining if the Hessian of the corresponding Largrangian is copositive over a set. To find the corresponding Lagrangian multiplier, two linear conic programming problems are constructed and then relaxed for computational purpose. Under the new condition, we proposed a local search based scheme to find a global optimal solution and showed its effectiveness by three examples.