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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao https://doi.org/10.1...arrow_drop_down
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
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The impact of scaling on simplex type algorithms

Authors: Nikolaos Ploskas; Nikolaos Samaras;

The impact of scaling on simplex type algorithms

Abstract

One of the most significant and well-studied optimization problems is the Linear Programming problem (LP). Many algorithms have been proposed for the solution of Linear Programming problems (LPs); the main categories of them are: (i) simplex-type or pivoting algorithms, (ii) interior-point methods (IPM) and (iii) exterior point simplex type algorithms (EPSA). Prior to the application of these algorithms, some preconditioning techniques are executed in order to improve the computational properties of LPs. Scaling is the most widely used preconditioning technique and is used to reduce the condition number of the constraint matrix, reduce the number of iterations required to solve LPs and improve the numerical behavior of the algorithms.The aim of this paper is to present a computational study of the impact of scaling prior to the application of the aforementioned algorithms. In the computational study that we have conducted, we calculate both the CPU time and the number of iterations with and without scaling for a set of sparse randomly generated optimal LPs. The scaling techniques that we applied to the above mentioned algorithms are: (i) arithmetic mean, (ii) equilibration, and (iii) geometric mean scaling techniques. Computational results showed that equilibration is the best scaling technique and that the effect of scaling is significant to IPM and revised simplex algorithm, while EPSA is scaling invariant.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
4
Average
Average
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