Convex Sets

  • Hoang Tuy
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 22)

Abstract

Let a, b be two points of R n. The set of all xR n of the form
$$x = \left( {1 - \lambda } \right)a + \lambda b = a + \left( {b - a} \right),\lambda \in R$$
(1.1)
is called the line through a and b. A subset M of R n is called an affine set (or affine manifold) if it contains every line through any two points of it, i.e. if (1 — λ)a + λbM for every aM, bM and every λ ∈ R. An affine set which contains the origin is a subspace.

Keywords

Extreme Point Convex Cone Closed Convex Cone Supporting Hyperplane Recession Cone 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Hoang Tuy
    • 1
  1. 1.Institute of MathematicsHanoiVietnam

Personalised recommendations