The Inverse Problems of some Mathematical Programming Problems

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.