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A Monotonic BuildUp Simplex Algorithm for Linear Programming
, 1991
"... We devise a new simplex pivot rule which has interesting theoretical properties. Beginning with a basic feasible solution, and any nonbasic variable having a negative reduced cost, the pivot rule produces a sequence of pivots such that ultimately the originally chosen nonbasic variable enters the ba ..."
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We devise a new simplex pivot rule which has interesting theoretical properties. Beginning with a basic feasible solution, and any nonbasic variable having a negative reduced cost, the pivot rule produces a sequence of pivots such that ultimately the originally chosen nonbasic variable enters the basis, and all reduced costs which were originally nonnegative remain nonnegative. The pivot rule thus monotonically builds up to a dual feasible, and hence optimal, basis. A surprising property of the pivot rule is that the pivot sequence results in intermediate bases which are neither primal nor dual feasible. We prove correctness of the procedure, give a geometric interpretation, and relate it to other pivoting rules for linear programming.
Parametric linear programming and anticycling pivoting rules
 MATHEMATICAL PROGRAMMING
, 1988
"... The traditional perturbation (or lexicographic) methods for resolving degeneracy in linear programming impose decision rules that eliminate ties in the simplex ratio rule and, therefore, restrict the choice of exiting basic variables. Bland's combinatorial pivoting rule also restricts the choic ..."
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Cited by 2 (0 self)
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The traditional perturbation (or lexicographic) methods for resolving degeneracy in linear programming impose decision rules that eliminate ties in the simplex ratio rule and, therefore, restrict the choice of exiting basic variables. Bland's combinatorial pivoting rule also restricts the choice of exiting variables. Using ideas from parametric linear programming, we develop anticycling pivoting rules that do not limit the choice of exiting variables beyond the simplex ratio rule. That is, any variable that ties for the ratio rule can leave the basis. A similar approach gives pivoting rules for the dual simplex method that do not restrict the choice of entering variables.
Technical Report Linear Programming 1
, 1997
"... Dedicated to George Dantzig on this the 50 th ..."
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"... or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the priorpermission of the copyright owner. ISBN: 0 444 70136 2 Publishers: ..."
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or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the priorpermission of the copyright owner. ISBN: 0 444 70136 2 Publishers:
Evaluation of Polynomials through the Simplex Algorithm.
, 1996
"... : This paper presents a method based on the simplex algorithm to evaluate real or complex polynomials, having scalar or interval coefficients. The aim of this method is not to find exactly the set P(X) where P is a polynomial and X a real interval or a complex disk but to obtain a set which surely c ..."
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: This paper presents a method based on the simplex algorithm to evaluate real or complex polynomials, having scalar or interval coefficients. The aim of this method is not to find exactly the set P(X) where P is a polynomial and X a real interval or a complex disk but to obtain a set which surely contains P(X). Keywords: interval computation, simplex algorithm, range of polynomials (R'esum'e : tsvp) Institut de Recherche en Informatique et Syst`emes Al'eatoires  email:obeaumon@irisa.fr CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE Centre National de la Recherche Scientifique Institut National de Recherche en Informatique (URA 227) Universit e de Rennes 1  Insa de Rennes et en Automatique  unit e de recherche de Rennes Evaluation de polynomes avec l'agorithme du Simplexe. R'esum'e : Nous pr'esentons ici une m'ethode, fond'ee sur l'agorithme du simplexe, pour 'evaluer des polynomes r'eels ou complexes, que leurs coefficients soient des scalaires ou des intervalles. Notre obj...