On Some Properties of Quadratic Programs with a Convex Quadratic Constraint

نویسندگان

  • Stefano Lucidi
  • Laura Palagi
  • Massimo Roma
چکیده

In this paper we consider the problem of minimizing a (possibly nonconvex) quadratic function with a quadratic constraint. We point out some new properties of the problem. In particular, in the rst part of the paper, we show that (i) given a KKT point that is not a global minimizer, it is easy to nd a \better" feasible point; (ii) strict complementarity holds at the local-nonglobal minimizer. In the second part, we show that the original constrained problem is equivalent to the unconstrained minimization of a piecewise quartic merit function. Using the unconstrained formulation we give, in the nonconvex case, a new second order necessary condition for global minimizers. In the third part, algorithmic applications of the preceding results are brieey outlined and some preliminary numerical experiments are reported.

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عنوان ژورنال:
  • SIAM Journal on Optimization

دوره 8  شماره 

صفحات  -

تاریخ انتشار 1998