This preview shows pages 1–6. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Introduction to Mathematical Programming IE406 Lecture 12 Dr. Ted Ralphs IE406 Lecture 12 1 Reading for This Lecture Bertsimas 4.84.9 IE406 Lecture 12 2 Polyhedral Cones Definition 1. A set C R n is a cone if x C for all and all x C . Definition 2. A polyhedron of the form P = { x R n  Ax } is called a polyhedral cone . Theorem 1. Let C R n be the polyhedral cone defined by the matrix A . Then the following are equivalent: 1. The zero vector is an extreme point of C . 2. The cone C does not contain a line. 3. The rows of A span R n . IE406 Lecture 12 3 Comments on Polyhedral Cones Notice that the origin is a member of every polyhedral cone. Furthermore, the origin is the only possible extreme point. A polyhedral cone that has the origin as an extreme point is called pointed . Graphically, a pointed cone looks like what we would ordinarily call a cone. IE406 Lecture 12 4 The Recession Cone Consider a nonempty polyhedron P = { x...
View
Full
Document
This note was uploaded on 08/06/2008 for the course IE 406 taught by Professor Ralphs during the Fall '08 term at Lehigh University .
 Fall '08
 Ralphs

Click to edit the document details