This paper first presents an improve cutting plane method for solving the linear programming problems, based on the primal simplex method with the current equivalent facet technique, in which the increment of objection function is allowed as a pivot variable to decide the search step size. We obtain a strong valid inequality from the objective increment model so as to find a better integer feasible solution in the discrete integral equivalent face. Then we propose a branch and cut for the quadratic integer programs. A example shows that it is superior to other approaches to solving $IQP$ problems.
School of Mathematics and Statistics, Wuhan university,China. 12/2004