ON SOME PROPERTIES OF QUADRATIC PROGRAMS WITH A CONVEX QUADRATIC CONSTRAINT

In this paper we consider the problem of minimizing a (possibly noncon vex) quadratic function with a quadratic constraint. We point out some new properties of the problem. In particular, in the first part of th e paper, we show that (i) given a KKT point that is not a global minim izer, it is easy to find a ''better'' feasible point; (ii) strict comp lementarity holds at the local-nonglobal minimizer. In the second part of this paper, we show that the original constrained problem is equiv alent to the unconstrained minimization of a piecewise quartic merit f unction. Using the unconstrained formulation we give, in the nonconvex case, a new second order necessary condition for global minimizers. I n the third part of this paper, algorithmic applications of the preced ing results are briefly outlined and some preliminary numerical experi ments are reported.