Cones, Matrices and Mathematical Programming

  • Abraham Berman

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 79)

Table of contents

  1. Front Matter
    Pages I-V
  2. Abraham Berman
    Pages 1-27
  3. Abraham Berman
    Pages 28-48
  4. Abraham Berman
    Pages 49-84
  5. Back Matter
    Pages 85-98

About this book

Introduction

This monograph is a revised set of notes on recent applications of the theory of cones, arising from lectures I gave during my stay at the Centre de recherches mathematiques in Montreal. It consists of three chapters. The first describes the basic theory. The second is devoted to applications to mathematical programming and the third to matrix theory. The second and third chapters are independent. Natural links between them, such as mathematical programming over matrix cones, are only mentioned in passing. The choice of applications described in this paper is a reflection of my p«r9onal interests, for examples, the complementarity problem and iterative methods for singular systems. The paper definitely does not contain all the applications which fit its title. The same remark holds for the list of references. Proofs are omitted or sketched briefly unless they are very simple. However, I have tried to include proofs of results which are not widely available, e.g. results in preprints or reports, and proofs, based on the theory of cones, of classical theorems. This monograph benefited from helpful discussions with professors Abrams, Barker, Cottle, Fan, Plemmons, Schneider, Taussky and Varga.

Keywords

Finite Matrices optimization programming proof theorem

Authors and affiliations

  • Abraham Berman
    • 1
  1. 1.Centre de Recherches Mathématiques, Montréal and Department of MathematicsIsrael Institute of TechnologyHaifaIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-80730-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 1973
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-06123-6
  • Online ISBN 978-3-642-80730-5
  • Series Print ISSN 0075-8442
  • About this book