L22 - CO350 Linear Programming Chapter 8: Degeneracy and...

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Unformatted text preview: CO350 Linear Programming Chapter 8: Degeneracy and Finite Termination 22th June 2005 Chapter 8: Finite Termination 1 Recap On Monday, we established In the absence of degeneracy, the simplex method will terminate after a nite number of iterations. The following observations 1. Iteration degenerate = ) old tableau degenerate. The converse is not true. 2. Iteration degenerate = ) new tableau degenerate. The converse is not true. 3. More than one choice of leaving variable = ) new basis degenerate. The converse is not true. 4. Iteration is degenerate () basic solution remains the same. Chapter 8: Finite Termination 2 Example of degeneracy (pg 105)- x 1 6 x 2 A AU C C O x 1- x 2 6 (0 ; 0) (0 ; 1) (1 ; 2) (1 ; 0) Feasible region H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H x 1 + x 2 = z x 1 + x 2 1 x 1 2 x 2 1 x 1 1 LP problem: max z = x 1 + x 2 s.t. x 1 + x 2 1 x 1 2 x 2 1 x 1 1 x 1 ; x 2 Chapter 8: Finite Termination 3 Geometry of degeneracy (bottom of pg 106) From the example: degeneracy in 2-dimension is represented by having more than two lines intersecting at an extreme point. = ) there is a redundant constraint. In general: degeneracy in d-dimension is represented by having more than d hyperplanes intersecting at an extreme point....
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This note was uploaded on 06/11/2011 for the course C 350 taught by Professor Wolkowicz during the Fall '97 term at Waterloo.

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L22 - CO350 Linear Programming Chapter 8: Degeneracy and...

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