Implementing the simplex method as a cutting-plane method, with a view to regularization

Authors:
Csaba I. Fábián;Olga Papp;Krisztián Eretnek
Affiliations:
Department of Informatics, Faculty of Mechanical Engineering and Automation, Kecskemét College, Kecskemét, Hungary 6000 and Doctoral School in Mathematics, Eötvös Loránd U ...;Department of Informatics, Faculty of Mechanical Engineering and Automation, Kecskemét College, Kecskemét, Hungary 6000 and Doctoral School in Mathematics, Eötvös Loránd U ...;Faculty of Informatics, Eötvös Loránd University, Budapest, Hungary
Venue:
Computational Optimization and Applications
Year:
2013

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Abstract

We show that the simplex method can be interpreted as a cutting-plane method, assuming that a special pricing rule is used. This approach is motivated by the recent success of the cutting-plane method in the solution of special stochastic programming problems.We focus on the special linear programming problem of finding the largest ball that fits into a given polyhedron. In a computational study we demonstrate that ball-fitting problems have such special characteristics which indicate their utility in regularization schemes.