Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

Extreme point

Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_322

A point in a convex set that cannot be expressed as a convex combination of two other distinct points in the set. Extreme points are also known as corner points or vertices. The extreme points of a rectangle are its four vertices, while the extreme points of a circular disc are the points on its circumference. For a linear programming problem, the extreme points of its convex set of solutions correspond to basic feasible solutions, and it can be shown that, if the problem has a finite optimal solution, then one of the extreme points is optimal.

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© Kluwer Academic Publishers 2001

Authors and Affiliations

  1. 1.Robert H. Smith School of BusinessUniversity of MarylandCollege PartUSA
  2. 2.School of Information Technology & EngineeringGeorge Mason UniversityFairfaxUSA