A regularized simplex method

Csaba Fábián (), Krisztián Eretnek and Olga Papp

Central European Journal of Operations Research, 2015, vol. 23, issue 4, 877-898

Abstract: In case of a special problem class, the simplex method can be implemented as a cutting-plane method that approximates a polyhedral convex objective function. In this paper we consider a regularized version of this cutting-plane method, and interpret the resulting procedure as a regularized simplex method. (Regularization is performed in the dual space and only affects the process through the pricing mechanism. Hence the resulting method moves among basic solutions.) We present algorithmic details of this regularized simplex method, and favorable test results with our implementation. For general linear programming problems, we propose a Newton-type approach which requires the solution of a sequence of special problems. Copyright Springer-Verlag Berlin Heidelberg 2015

Keywords: Linear programming; Convex programming; Simplex method; Cutting-plane methods; Regularization (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10100-014-0344-9

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