Lecture12 - Introduction to Mathematical Programming IE406...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Introduction to Mathematical Programming IE406 Lecture 12 Dr. Ted Ralphs IE406 Lecture 12 1 Reading for This Lecture Bertsimas 4.8-4.9 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 .

Page1 / 12

Lecture12 - Introduction to Mathematical Programming IE406...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online