Analysis of mathematical programming problems prior to applying the simplex algorithm

Brearley, A. L.; Mitra, Gautam; Williams, H. Paul

doi:10.1007/bf01580428

Cited by 237 publications

(105 citation statements)

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“…Note that the end points of arc-search algorithm (23) and (24) are equat to the end points of Mehrotra's formulae in (25) and (26); for…”

Section: End (For)mentioning

confidence: 99%

“…We will address all of these implementation topics and provide detailed information of our implementation. As we will compare arc-search method and Mehrotra's method, to make a meaningful and fair comparison, we will implement everything discussed in this section the same way for both methods, so that the only differences of the two algorithms in our implementations are in Steps 4 and 5, where the arc-search method uses formulae (23) and (24) and Mehrotra's method uses (25) and (26). But the difference of the computational cost is very small because these computations are all analytic.…”

Section: Implementation Detailsmentioning

confidence: 99%

“…Many literatures have been focused on this topic, for example, [1,7,25,26,27]. As we will test all linear programming problems in standard form in Netlib, we focus on the strategies only for the standard linear programming problems in the form of (1) and solved in normal equations 2 .…”

Section: Pre-processmentioning

confidence: 99%

“…The first part f obj at the beginning is zero and is updated all the time as we reduce the problem (remove some c k from c); the terms in the summation in the second part are continuously reduced and c k are updated as necessary when we reduce the problem. The first 6 pre-process methods presented below were reported in various literatures, such as [1,17,25,26,27]; the rest of them, to the best of our knowledge, are not reported anywhere. …”

Section: Pre-processmentioning

confidence: 99%

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CurveLP-A MATLAB implementation of an infeasible interior-point algorithm for linear programming

Yang¹

2016

Numer Algor

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Mehrotra's algorithm has been the most successful infeasible interior-point algorithm for linear programming since 1990. Most popular interior-point software packages for linear programming are based on Mehrotra's algorithm. This paper proposes an alternative algorithm, arc-search infeasible interior-point algorithm. We will demonstrate, by testing Netlib problems and comparing the test results obtained by arc-search infeasible interior-point algorithm and Mehrotra's algorithm, that the proposed arc-search infeasible interior-point algorithm is a more efficient algorithm than Mehrotra's algorithm.

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“…Note that the end points of arc-search algorithm (23) and (24) are equat to the end points of Mehrotra's formulae in (25) and (26); for…”

Section: End (For)mentioning

confidence: 99%

Section: Implementation Detailsmentioning

confidence: 99%

Section: Pre-processmentioning

confidence: 99%

Section: Pre-processmentioning

confidence: 99%

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CurveLP-A MATLAB implementation of an infeasible interior-point algorithm for linear programming

Yang¹

2016

Numer Algor

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“…The author briefly described these routines and their implementations, and gives some results of their application to small LPs. The reader concerned with redundancy in large LPs must look further; however, a good reference to start with is the first part of "Analysis of mathematical programming problems prior to applying the simplex algorithm" by A. L. Brearly, G. Mitra and H. P. Williams [1975].…”

Section: Referencesmentioning

confidence: 99%

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Formulating processing network models: Viability theory

Chinneck¹

1990

Naval Research Logistics

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A processing network contains at least one processing node; such a node is constrained by fixed ratios of flow in it's terminals. Though fast solution algorithms are available, processing network models are difficult to formulate in the first place so that meaningful results are obtained. Until now, there have been no automated aids for use during the model‐building phase. This article develops the theory of model viability and presents the first such aid: an algorithm for the identification and localization of a class of errors which can occur during model formulation.

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Analysis of mathematical programming problems prior to applying the simplex algorithm

Cited by 237 publications

References 3 publications

CurveLP-A MATLAB implementation of an infeasible interior-point algorithm for linear programming

CurveLP-A MATLAB implementation of an infeasible interior-point algorithm for linear programming

Book Reviews

Formulating processing network models: Viability theory

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