Phase I cycling under the most-obtuse-angle pivot rule

Guerrero-Garcı́a, Pablo; Santos-Palomo, Ángel

doi:10.1016/j.ejor.2003.06.048

Cited by 33 publications

(1 citation statement)

References 6 publications

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“…In other words, cycling can only occur in full iterations. This algorithm belong to the class of 'infinite' algorithms, since the possibility of cycling cannot be ruled out theoretically at present; in fact, a cycling example has been recently given by Cuerrero-Garcfa and SantosPalomo [11] in the classical context. From a practical point of view, finiteness is not a serious problem: first, it is well known that computational performance of existing 'finite' simplex variants is unsatisfactory whereas successful simplex variants are actually 'infinite', such as Dantzig's conventional simplex method.…”

Section: Comments On the Pivoting Rulementioning

confidence: 97%

A basis-deficiency-allowing primal phase-I algorithm using the most-obtuse-angle column rule

Guerrero-Garcı́a

Santos-Palomo

2006

Computers & Mathematics with Applications

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The dual Phase-I algorithm using the most-obtuse-angle row pivot rule is very efficient for providing a dual feasible basis, in either the classical or the basis-deficiency-allowing context. In this paper, we establish a basis-deficiency-allowing Phase-I algorithm using the so-called most-obtuseangle column pivot rule to produce a primal (deficient or full) basis. Our computational experiments with the smallest test problems from the standard NETLIB set show that a dense projected-gradient implementation largely outperforms that of the variation of the primal simplex method from the commercial code MATLAB LINPROG vl.17, and that a sparse projected-gradient implementation of a normalized revised version of the proposed algorithm runs 34°~ faster than the sparse implementation of the primal simplex method included in the commercial code TOMLAB LPSOLVE V3.0. (~)

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Section: Comments On the Pivoting Rulementioning

confidence: 97%