A Modification of Quadratic Programming Algorithm

In the existing methods for solving Quadratic Programming Problems having linearly factorized objective function and linear constraints, all the linear factors of the objective function are supposed to be positive for all feasible solutions. Here, a modification of the existing methods is proposed and it has been proved that the modified method can be applied to find the optimal solution of the problem even if all the linear factors of the objective function are not necessarily positive for all feasible solutions. Moreover, the proposed method can be applied to find the optimal solution of the problem even if the basic solution at any stage is not feasible. If the initial basic solution is feasible, we use simplex method to find the optimal solution. If the basic solution at any stage is not feasible, we use dual simplex method to find the optimal solution. Numerical examples are given to illustrate the method and the results are compared with the results obtained by other methods.