The use of grossone in Mathematical Programming and Operations Research

The concepts of infinity and infinitesimal in mathematics date back to ancients Greek and have always attracted great attention. Very recently, a new methodology has been proposed by Sergeyev [10] for performing calculations with infinite and infinitesimal quantities, by introducing an infinite unit...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 218; no. 16; pp. 8029 - 8038
Main Authors: De Cosmis, Sonia, De Leone, Renato
Format: Journal Article
Language:English
Published: Elsevier Inc 15.04.2012
Subjects:
Infinity
Linear programming
Mathematical analysis
Mathematical models
Mathematical programming
Nonlinear programming
Operations research
Penalty methods
Simplex Method
Penalty methods
Linear programming
Simplex Method
Nonlinear programming
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:The concepts of infinity and infinitesimal in mathematics date back to ancients Greek and have always attracted great attention. Very recently, a new methodology has been proposed by Sergeyev [10] for performing calculations with infinite and infinitesimal quantities, by introducing an infinite unit of measure expressed by the numeral ① (grossone). An important characteristic of this novel approach is its attention to numerical aspects. In this paper we will present some possible applications and use of ① in Operations Research and Mathematical Programming. In particular, we will show how the use of ① can be beneficial in anti-cycling procedure for the well-known Simplex Method for solving Linear Programming problems and in defining exact differentiable penalty functions in Nonlinear Programming.
Bibliography:ObjectType-Article-2
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ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.07.042