Minimax Algebra

  • Raymond Cuninghame-Green

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 166)

Table of contents

  1. Front Matter
    Pages N2-XI
  2. Raymond Cuninghame-Green
    Pages 1-10
  3. Raymond Cuninghame-Green
    Pages 11-24
  4. Raymond Cuninghame-Green
    Pages 25-32
  5. Raymond Cuninghame-Green
    Pages 33-39
  6. Raymond Cuninghame-Green
    Pages 40-51
  7. Raymond Cuninghame-Green
    Pages 52-55
  8. Raymond Cuninghame-Green
    Pages 56-61
  9. Raymond Cuninghame-Green
    Pages 62-71
  10. Raymond Cuninghame-Green
    Pages 72-76
  11. Raymond Cuninghame-Green
    Pages 77-85
  12. Raymond Cuninghame-Green
    Pages 86-92
  13. Raymond Cuninghame-Green
    Pages 93-99
  14. Raymond Cuninghame-Green
    Pages 100-111
  15. Raymond Cuninghame-Green
    Pages 112-118
  16. Raymond Cuninghame-Green
    Pages 119-129
  17. Raymond Cuninghame-Green
    Pages 130-140
  18. Raymond Cuninghame-Green
    Pages 141-146
  19. Raymond Cuninghame-Green
    Pages 147-153
  20. Raymond Cuninghame-Green
    Pages 154-161

About this book

Introduction

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or approximately, the eigenvector­ eigenvalue problem andso on.Some of this material contains results of hitherto unpublished research carried out by the writer during the years 1970-1977.

Keywords

Lineare Algebra convex analysis graph theory inequality linear optimization network networks optimization programming research scheduling transformation transport transportation value-at-risk

Authors and affiliations

  • Raymond Cuninghame-Green
    • 1
  1. 1.Dept. of Mathematical StatisticsUniversity of BirminghamBirminghamEngland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-48708-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 1979
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-09113-4
  • Online ISBN 978-3-642-48708-8
  • Series Print ISSN 0075-8442
  • About this book