Lecture25 - IE 495 Lecture 25 Reading for This Lecture...

Info iconThis preview shows pages 1–7. 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 Document Right Arrow Icon

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

View Full Document Right Arrow Icon

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

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

Unformatted text preview: IE 495 Lecture 25 November 30, 2000 Reading for This Lecture Primary ¡ Bazaraa, Sherali, and Sheti, Chapter 2. ¡ Chvatal, Chapters 6 and 7. Linear Programming Introduction Consider again the system Ax = b, A ∈ R m × n , b ∈ R m . In this problem, there are either ¡ no solutions ¡ one solution ¡ infinitely many solutions (if n > m) The problem of linear programming is min c T x s.t. Ax = b x ≥ 0 The Simplex Algorithm Note that x B = B-1 b - B-1 Nx N Hence, c T x = c B T x B + c N T x N = c B T B-1 b + ( c N T- c B T B-1 N)x N So if c N T- c B T B-1 N ≥ , we have found the optimal solution (why?). Otherwise, suppose some component of c N T- c B T B-1 N is negative. Then we raise the value of the corresponding variable as much as possible while maintaining feasibility. Summary of the Simplex Algorithm Simplex algorithm ¡ Compute yB = c B T ¡ Choose a column of a j of N such ya j < c j ¡ Compute Bd = a j ¡ Find the largest t such that x B * - td ≥ 0 ¡ Set the value of x j to t and the values of the basic variables to x B * - td ....
View Full Document

{[ snackBarMessage ]}

Page1 / 18

Lecture25 - IE 495 Lecture 25 Reading for This Lecture...

This preview shows document pages 1 - 7. Sign up to view the full document.

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