© 2013

Discrete Geometry and Optimization

  • Karoly Bezdek
  • Antoine Deza
  • Yinyu Ye
  • Contains a wide range of open problems, novel results, and state-of-the-art surveys

  • Presents a snapshot of a rapidly evolving area on the boundary of discrete geometry and optimization

  • Reflects the broad and international participation at the Workshop on Discrete Geometry, Conference on Discrete Geometry and Optimization, and Workshop on Optimization


Part of the Fields Institute Communications book series (FIC, volume 69)

Table of contents

  1. Front Matter
    Pages i-x
  2. Javier Alonso, Horst Martini, Margarita Spirova
    Pages 1-15
  3. Miguel F. Anjos, Frauke Liers, Gregor Pardella, Andreas Schmutzer
    Pages 17-32
  4. Katherine Burggraf, Jesús De Loera, Mohamed Omar
    Pages 55-77
  5. Adrian Dumitrescu, Günter Rote, Csaba D. Tóth
    Pages 79-104
  6. Marianna E.-Nagy, Monique Laurent, Antonios Varvitsiotis
    Pages 105-120
  7. Frédéric Meunier, Antoine Deza
    Pages 179-190
  8. Bojan Mohar, Tamon Stephen
    Pages 191-211
  9. Vincent Pilaud, Christian Stump
    Pages 213-248
  10. Franz Rendl, Abdel Lisser, Mauro Piacentini
    Pages 249-263
  11. Achill Schürmann
    Pages 265-278
  12. Davood Shamsi, Nicole Taheri, Zhisu Zhu, Yinyu Ye
    Pages 279-301
  13. Negar Soheili, Javier Peña
    Pages 303-320
  14. Károly Bezdek, Antoine Deza, Yinyu Ye
    Pages 321-336

About this book


​​Optimization has long been a source of both inspiration and applications for geometers, and conversely, discrete and convex geometry have provided the foundations for many optimization techniques, leading to a rich interplay between these subjects. The purpose of the Workshop on Discrete Geometry, the Conference on Discrete Geometry and Optimization, and the Workshop on Optimization, held in September 2011 at the Fields Institute, Toronto, was to further stimulate the interaction between geometers and optimizers. This volume reflects the interplay between these areas.

The inspiring Fejes Tóth Lecture Series, delivered by Thomas Hales of the University of Pittsburgh, exemplified this approach. While these fields have recently witnessed a lot of activity and successes, many questions remain open. For example, Fields medalist Stephen Smale stated that the question of the existence of a strongly polynomial time algorithm for linear optimization is one of the most important unsolved problems at the beginning of the 21st century. The broad range of topics covered in this volume demonstrates the many recent and fruitful connections between different approaches, and features novel results and state-of-the-art surveys as well as open problems.


Carathéodory theorem Combinatorics Eigenvalue optimization Minkowski spaces SDP relaxation polyhedral computations

Editors and affiliations

  • Karoly Bezdek
    • 1
  • Antoine Deza
    • 2
  • Yinyu Ye
    • 3
  1. 1., Mathematics & StatisticsUniversity of CalgaryCalgaryCanada
  2. 2., Department of ComputingMcMaster UniversityHamiltonCanada
  3. 3.School of Engineering, Department of Management Science and EngStanford UniversityStanfordUSA

Bibliographic information