Minimax Algebra (Lecture Notes in Economics and Mathematical Systems, 166)

Cuninghame-Green, R. A.

ISBN 10: 3540091130 / ISBN 13: 9783540091134

Published by Springer, 1979

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Bibliographic Details

• Title: Minimax Algebra (Lecture Notes in Economics and Mathematical Systems, 166)
• Publisher: Springer
• Publication Date: 1979
• Language: English
• ISBN 10: 3540091130
• ISBN 13: 9783540091134
• Binding: Paperback
• Condition: Very Good
• Dust Jacket Condition: Dust Jacket Included
• Book Type: book

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Synopsis

A number of different problems of interest to the operational researcher and the mathematical economist - for example, certain problems of optimization on graphs and networks, of machine-scheduling, of convex analysis and of approx­ imation theory - can be formulated in a convenient way using the algebraic structure (R,$,@) where we may think of R as the (extended) real-number system with the binary combining operations x$y, x®y defined to be max(x,y),(x+y) respectively. The use of this algebraic structure gives these problems the character of problems of linear algebra, or linear operator theory. This fact hB.s been independently discovered by a number of people working in various fields and in different notations, and the starting-point for the present Lecture Notes was the writer's persuasion that the time had arrived to present a unified account of the algebra of linear transformations of spaces of n-tuples over (R,$,®),to demonstrate its relevance to operational research and to give solutions to the standard linear-algebraic problems which arise - e.g. the solution of linear equations exactly or approximately, the eigenvector­ eigenvalue problem andso on.Some of this material contains results of hitherto unpublished research carried out by the writer during the years 1970-1977.