In this paper, we propose to minimize a convex quadratic problem with bounded variables. The
used method, known as adaptive, takes into account the specificities of the problem and treats the
constraints such as presented. Instead of using the standard direction, which takes only nul or extreme
values, we will suggest here a new descent direction, called hybrid direction. The latter takes
extreme values for some relatively big components of the reduced costs vector and it takes the values
of the anti-gradient for the other components. On the basic of this new concept, we construct an
algorithm for solving the problem. Finally a numerical example is given for illustration purpose.