Showing papers by "University of Ljubljana, Faculty of Economics published in 1993"
TL;DR: This paper discusses some instances where dense matrix techniques can be utilized within a sparse simplex linear programming solver and describes a variant of this method which uses updating of the QR factorization of the Schur complement matrix.
Abstract: In this paper we discuss some instances where dense matrix techniques can be utilized within a sparse simplex linear programming solver. The main emphasis is on the use of the Schur complement matrix as a part of the basis matrix representation. This approach enables to represent the basis matrix as an easily invertible sparse matrix and one or more dense Schur complement matrices. We describe our variant of this method which uses updating of the QR factorization of the Schur complement matrix. We also discuss some implementation issues of the LP software package which is based on this approach.
3 citations
01 Jan 1993
TL;DR: The primal-dual interior point algorithm (LPINT) as discussed by the authors is an LP software package based on Karmarkar's algorithm, which is a competitive method for solving linear programming problems.
Abstract: Karmarkar’s algorithm (Karmarkar 1984) and other interior point methods are now regarded as a competitive methods for solving linear programming (LP) problems. It is therefore worth-while to undertake development of a professional LP software based on some particular interior point method. We describe design and implementation aspects of LPINT, an LP software package which is based on the primal-dual interior point algorithm.