AN EXTENSION OF GENERALIZED UPPER BOUNDED TECHNIQUES FOR LINEAR PROGRAMMING

Abstract : The paper by Dantzig and Wolfe (Decomposition Principle for Linear Programs) suggested the need for developing new techniques for solving linear programming problems with a special matrix structure. A number of techniques have appeared since then. In this report, an algorithm for solving a structured linear programming problem with a very large number of blocks is given. The main feature of the method as described in another work (Generalized Upper Bounding Techniques for Linear Programming, II) is to carry out the computation with the help of a smaller basis whose order is equal to the number of linking equations coupling together the various blocks. (Author)