A method for approximating the solution set of a system of convex inequalities by polytopes

Research output: Contribution to journalArticlepeer-review

Abstract

In this note a method for computing approximating by polytopes of the solution set Q of a system of convex inequalities is presented. It is shown that such approximations can be determined by an algorithm which converges in finitely many steps when the solution set of the given system of inequalities is bounded. In this case, the algorithm generates "inner" and "outer" approximations having the Hausdorff distance to each other (and to the set Q) no greater than an a priori fixed ε{lunate} and having their extreme points in ∂Q and in the relative exterior of Q, respectively.

Original languageEnglish
Pages (from-to)289-304
Number of pages16
JournalJournal of Computational and Applied Mathematics
Volume36
Issue number3
DOIs
StatePublished - 24 Sep 1991

Keywords

  • Hausdorff metric
  • Simplex
  • convex set
  • g-marginal vertex
  • polytope
  • refinement of a triangulation
  • triangulation

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'A method for approximating the solution set of a system of convex inequalities by polytopes'. Together they form a unique fingerprint.

Cite this