Implementation of The Extended Dantzig – Wolfe Method

In this paper implementation of the extended Dantzig- Wolfe method to solve a general quadratic programming problem is presented,that is, obtaining a local minimum of a quadratic function subject to inequality constraints. The method terminates successfully at a KT point in a finite number of steps. No extra effort is needed when the function is non-convex. The method solve convex quadratic programming problems. It is a simplex like procedure to the Dantzig- Wolfe method[1]. So, it is, the same as the Dantzig – Wolfe method when the Hessian matrix of the quadratic function is positive definite[7]. The obvious difference between our method and the Dnatzig – Wolfe method is in the possibility of decreasing the complement of the new variable that has just become non-basic. In the practical implementation of the method we inherit the computational features of the active set methods using the matrices H, U and T, and in particular the stable features [5]. The features (i.e, the stable features) are achieved by using orthogonal factorizations of the matrix of active constraints when the tableau is complementary. In our work we give full description to an algorithm applying the extended Dantzig-wolfe method as a model of th