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Implementing the simplex method as a cutting-plane method

Csaba I. Fabian(fabian.csaba***at***gamf.kefo.hu)
Olga Papp(papp.olga***at***gamf.kefo.hu)
Krisztian Eretnek(eretnek.krisztian***at***gmail.com)

Abstract: We show that the simplex method can be interpreted as a cutting-plane method, assumed 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 compare the classic Dantzig pricing rule and the rule that derives from the cutting-plane approach. We focus on the special linear programming problem of finding the largest ball that fits into a given polyhedron.

Keywords: Simplex method, cutting-plane method, linear programming, convex programming, stochastic programming.

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Convex and Nonsmooth Optimization


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Entry Submitted: 06/30/2011
Entry Accepted: 07/03/2011
Entry Last Modified: 06/30/2011

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