Triangular Factorization and Generalized Upper Bounding Techniques

Abstract

We develop a compact inverse method for linear programming problems having block triangular or sparse constraint matrices. Special cases of the method are, for example, the generalized upper bounding technique and its extensions. For these methods we show how a triangular factorization can be used for the working basis and block bases. In this case (and even if the constraint matrix has no special structure) our method becomes a variation of the revised simplex method using a single triangular factorization of the basis. However, the updating procedure of the triangular factors differs from existing ones in a way that implies that certain structures are exploited naturally.