Implementation Of The Extended Dantzig - Wolfe Method

Abstract

Abstract In this thesis an implementation of the extended Dantzig - Wolfe method to solve a general quadratic programming problem (that is, obtaining a local minimum of a quadratic function subject to inequality constraints) is presented. 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. So it is a simplex like procedure to the Dantzig - Wolfe method. So it is, the same as the Dantzig — Wolfe _method‘_when tl1f_e_;'_IjIessia11 matrix of the quadratic function is positive definite. 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 feat11r_es'(see-Gvilltancl Murray (1978)). The features (i.e, the stqble, features) are achieved by using orthogonal factorizations of the matrix of active constraints when the tableau is complementary.