rs_part2 - ORIE 3300/5300 Optimization Professor Bland Fall...

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ORIE 3300/5300 Optimization Fall 2011 Professor Bland Example of the Revised Simplex Method: Part 2 Part II: Using Product Form of the Inverse Let’s review the 3 simplex pivots we did earlier using the revised simplex method with the explicit basis inverse. 1st pivot column 2nd pivot column 3rd pivot column 1 1 ± - 1 0 1 1 ± 1 ± - 1 0 E 1 = 1 0 - 1 0 1 0 0 0 1 E 2 = 1 0 0 - 1 1 0 1 0 1 E 3 = 1 1 0 0 1 0 0 0 1 A - 1 B = E 1 A - 1 B = E 2 E 1 A - 1 B = E 3 E 2 E 1 η 1 = - 1 0 1 , ρ 1 = 3 η 2 = 1 - 1 1 , ρ 2 = 1 η 3 = 1 1 0 , ρ 3 = 2 Suppose we add a new variable x 11 with A 11 = 1 1 2 c 11 = 8 . After the third pivot we had B = (2 , 10 , 1) , c B = (2 , 0 , 4) , b = 1 0 1 First calculate y = c B A - 1 B = ((( c B E 3 ) E 2 ) E 1 ) (2 , 0 , 4) (2 , 2 , 4) (4 , 2 , 4) (4 , 2 , 0) = y c 11 = c 11 - yA 11
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rs_part2 - ORIE 3300/5300 Optimization Professor Bland Fall...

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