a6 - CO350 Assignment 6 Wing Man Fok 20300650 June 25, 2010...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
CO350 Assignment 6 Wing Man Fok 20300650 , June 25 2010 : - Instructor Mathieu Guay Paquet 1a Suppose there is a tie for the choice of leaving variable in an iteration of the . simplex method , = = ∈ , , ∉ ≠ . That is t biaik bjajk for some k N i j B with i j Assume WLOG that the new = ∪ ∖ . , , basis is B' B k i When pivoting k i we subtract ajkaik times the xi row from . = - = . , the xj row So bj' bj ajkaikbi 0 Hence the new basic variable has value zero in , . - the new solution and B' is degenerate Since every perturbed LP is non , degenerate there is never a tie for the choice of leaving variable in the . , , perturbation method Otherwise the new basis is degenerate which is . impossible 2a Suppose there is an iteration of the simplex method which starts with basis B . > = - . =- and ends with basis B' We can find t 0 and Ak such that xB' xB tAk Let d . , = ( )= - = ( - )= . Ak Since B and B' are both feasible Ad 1tA td 1tAxB' AxB 1t b b 0 Also note that = = - > cTd 1tcTtd 1tcTxB' cTxB 0 = - = - > dk 1txB'k xBk 1txB'k 0 0 = - = - < dr 1txB'r xBr 1t0 xBr 0
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/28/2011 for the course CO 350 taught by Professor S.furino,b.guenin during the Fall '07 term at Waterloo.

Page1 / 4

a6 - CO350 Assignment 6 Wing Man Fok 20300650 June 25, 2010...

This preview shows document pages 1 - 2. Sign up to view the full document.

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