Algorithmic Aspects of Convex Sets: Formulation of the Problems

  • Martin Grötschel
  • László Lovász
  • Alexander Schrijver
Part of the Algorithms and Combinatorics book series (AC, volume 2)


Convex sets and convex functions are typical objects of study in mathematical programming, convex analysis, and related areas. Here are some key questions one encounters frequently:
  • Given a point y and a set K, is y a member of K, i. e., is y contained in K?

  • If y is not a member of K, find a hyperplane separating y from K.

  • Given a linear inequality, is it valid for each vector in K?

  • Given a linear function, find a point maximizing (or minimizing) the function on K.

  • Given a convex function, find its minimum.


Convex Body Rational Number Separation Problem Separation Algorithm Membership Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Martin Grötschel
    • 1
    • 2
  • László Lovász
    • 3
    • 4
  • Alexander Schrijver
    • 5
    • 6
  1. 1.Konrad-Zuse-Zentrum für Informationstechnik BerlinBerlinGermany
  2. 2.Fachbereich MathematikTechnische Universität BerlinBerlinGermany
  3. 3.Department of Computer ScienceEötvös Loránd UniversityBudapestHungary
  4. 4.Department of MathematicsYale UniversityNew HavenUSA
  5. 5.CWI (Center for Mathematics and Computer Science)AmsterdamThe Netherlands
  6. 6.Department of MathematicsUniversity of AmsterdamAmsterdamThe Netherlands

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