  The non-convex quadratic orogramming problem and the non-monotone linear
complementarity problem are NP-complete problems. In this paper we first show
taht the inverse problem of determinning a KKT point of the non-convex
quadratic programming problem is polynomial. We then show that the inverse
problems of non-monotone linear complementarity problem are polynomial solvable
in some cases, and in another case is NP-hard. Therefore we solve an open
question raised by Heuberger on inverse NP-hard problems and prove that
CoNP=NP.
