{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture23

Lecture23 - Advanced Mathematical Programming IE417 Lecture...

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 Document

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Advanced Mathematical Programming IE417 Lecture 23 Dr. Ted Ralphs IE417 Lecture 23 1 Reading for This Lecture • Chapter 10 IE417 Lecture 23 2 Linear Programming • We are given A ∈ R m × n , b ∈ R m . Assume S = { x ∈ R n s.t. Ax = b,x ≥ is bounded. • We want to solve the LP min c > x s.t. Ax = b x ≥ • We need only consider the extreme points. IE417 Lecture 23 3 Characterization of Extreme Points • Arrange the columns of A such that A = [ B,N ] , where B is a non- singular n × n matrix. • Then x is an extreme point of S if and only if x = [ x B , 0] where x B = B- 1 b for some arrangement such that B- 1 b ≥ • This implies that the number of extreme points is finite (but still potentially very large). IE417 Lecture 23 4 The Simplex Algorithm • Note that x B = B- 1 b- B- 1 Nx N • Hence, c > x = c > B x B + c- N > x N = c > B B- 1 b + ( c > N- c > B B- 1 N ) x N • So if c > N- c > B B- 1 N ≥ , we have found the optimal solution (why?) • Otherwise, suppose some component of c > N- c > B B- 1 N is negative.is negative....
View Full Document

{[ snackBarMessage ]}

Page1 / 12

Lecture23 - Advanced Mathematical Programming IE417 Lecture...

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

View Full Document
Ask a homework question - tutors are online