Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2010.1627.1631ChikhaouiA.DjebbarB.MekkiR.1220101015The aim of this study is to present a new method for finding an optimal solution to quadratic programming problems. The principle of the method is based on calculating the value of critical point. If the critical point belongs to the set of feasible solutions, so the optimal solution to our problem is the critical point itself. If the critical point is not at in the feasible solution set, a new feasible constraint set is built by a homographic transform, in such a way that the projection of the critical point of the objective function onto this set produces the exact solution to the problem on hand. It should be noted here that the objective function may be convex or not convex. On the other hand the search for the optimal solution is to find the hyper plane separating the convex and the critical point. Notice that one does not need to transform the quadratic problem into an equivalent linear one as in the numerical methods; the method is purely analytical and avoids the usage of initial solution. An algorithm computing the optimal solution of the concave function has given.]]>Achmanov, S.,1984Bierlaire, M.,2006De Werra, D., T.M. Liebling and J.F. Heche,2003De Klerk, E. and D.V. Pasechnik,2007Delbos, F. and J.C. Gilbert,2005Hillier, F.S. and G.J. Lieberman,2005Dozzi, M.,2004Simonnard, M.,1973Dong, S.,2006