Deterministic Global Optimization

Geometric Branch-and-bound Methods and their Applications

  • Daniel Scholz

Part of the Springer Optimization and Its Applications book series (SOIA, volume 63)

Also part of the Nonconvex Optimization and Its Applications book sub series (SOIANOIA, volume 63)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Daniel Scholz
    Pages 1-14
  3. Daniel Scholz
    Pages 15-24
  4. Daniel Scholz
    Pages 25-57
  5. Daniel Scholz
    Pages 59-71
  6. Daniel Scholz
    Pages 73-82
  7. Daniel Scholz
    Pages 83-96
  8. Daniel Scholz
    Pages 97-108
  9. Daniel Scholz
    Pages 109-116
  10. Daniel Scholz
    Pages 117-127
  11. Daniel Scholz
    Pages 129-132
  12. Back Matter
    Pages 133-142

About this book

Introduction

This monograph deals with a general class of solution approaches in deterministic global optimization, namely the geometric branch-and-bound methods which are popular algorithms, for instance, in Lipschitzian optimization, d.c. programming, and interval analysis.It also introduces a new concept for the rate of convergence and analyzes several bounding operations reported in the literature, from the theoretical as well as from the empirical point of view. Furthermore, extensions of the prototype algorithm for multicriteria global optimization problems as well as mixed combinatorial optimization problems are considered. Numerical examples based on facility location problems support the theory. Applications of geometric branch-and-bound methods, namely the circle detection problem in image processing, the integrated scheduling and location makespan problem, and the median line location problem in the three-dimensional space are also presented.

The book is intended for both researchers and students in the areas of mathematics, operations research, engineering, and computer science.

Keywords

Bounding Operation Branch and Bound Algorithm Circle Detection Problem Deterministic Global Optimization Median Line Problem Mixed Combinatorial Optimization Multicriteria Optimization Solution Approaches

Authors and affiliations

  • Daniel Scholz
    • 1
  1. 1., Institute for Numerical andGeorg-August-University GöttingenGöttingenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-1951-8
  • Copyright Information Springer Science+Business Media, LLC 2012
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-1950-1
  • Online ISBN 978-1-4614-1951-8
  • Series Print ISSN 1931-6828
  • About this book