Anstreicher-Terlaky type monotonic simplex algorithms for linear feasibility problems

Authors:
Filiz Bilen;Zsolt Csizmadia;Tibor Illés
Affiliations:
Department of Mathematics, Eastern Mediterranean University, Famagusta, North Cyprus;Department of Operations Research, Institute of Mathematics, Eötvös Loránd University, Hungary;Department of Operations Research, Institute of Mathematics, Eötvös Loránd University, Hungary
Venue:
Optimization Methods & Software
Year:
2007

Citing 4
Cited 0

A new polynomial-time algorithm for linear programming

Combinatorica
Polynomial expected behavior of a pivoting algorithm for linear complementarity and linear programming problems

Mathematical Programming: Series A and B
Criss-cross methods: a fresh view on pivot algorithms

Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Computational Techniques of the Simplex Method

Computational Techniques of the Simplex Method

Quantified Score

Hi-index	0.00

Visualization

Abstract

Based on the pivot selection rule [Anstreicher, K.M. and Terlaky, T., 1994, A monotonic build-up simplex algorithm for linear programming. Operations Research, 42, 556-561.] we define a new monotonic build-up (MBU) simplex algorithm for linear feasibility problems. An mK upper bound for the iteration bound of our algorithm is given under a weak non-degeneracy assumption, where K is determined by the input data of the problem and m is the number of constraints. The constant K cannot be bounded in general by a polynomial of the bit length of the input data since it is related to the determinants (of the pivot tableau) with the highest absolute value. An interesting local property of degeneracy led us to construct a new recursive procedure to handle strongly degenerate problems as well. Analogous complexity bounds for the linear programming versions of MBU and the first phase of the simplex method can be proved under our weak non-degeneracy assumption.