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Geometric Methods and Optimization Problems

  • V. Boltyanski
  • H. Martini
  • V. Soltan

Part of the Combinatorial Optimization book series (COOP, volume 4)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. V. Boltyanski, H. Martini, V. Soltan
    Pages 1-230
  3. V. Boltyanski, H. Martini, V. Soltan
    Pages 231-355
  4. V. Boltyanski, H. Martini, V. Soltan
    Pages 357-429
  5. Back Matter
    Pages 431-431

About this book

Introduction

VII Preface In many fields of mathematics, geometry has established itself as a fruitful method and common language for describing basic phenomena and problems as well as suggesting ways of solutions. Especially in pure mathematics this is ob­ vious and well-known (examples are the much discussed interplay between lin­ ear algebra and analytical geometry and several problems in multidimensional analysis). On the other hand, many specialists from applied mathematics seem to prefer more formal analytical and numerical methods and representations. Nevertheless, very often the internal development of disciplines from applied mathematics led to geometric models, and occasionally breakthroughs were b~ed on geometric insights. An excellent example is the Klee-Minty cube, solving a problem of linear programming by transforming it into a geomet­ ric problem. Also the development of convex programming in recent decades demonstrated the power of methods that evolved within the field of convex geometry. The present book focuses on three applied disciplines: control theory, location science and computational geometry. It is our aim to demonstrate how methods and topics from convex geometry in a wider sense (separation theory of convex cones, Minkowski geometry, convex partitionings, etc.) can help to solve various problems from these disciplines.

Keywords

Median Partition calculus computational geometry geometry linear optimization optimization

Authors and affiliations

  • V. Boltyanski
    • 1
  • H. Martini
    • 2
  • V. Soltan
    • 3
  1. 1.CIMATGuanajuatoMexico
  2. 2.Technical University, ChemnitzChemnitzGermany
  3. 3.Moldavian Academy of SciencesKishinevMoldova

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4615-5319-9
  • Copyright Information Springer-Verlag US 1999
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-7427-5
  • Online ISBN 978-1-4615-5319-9
  • Series Print ISSN 1388-3011
  • Buy this book on publisher's site