Lecture 9C

Lecture 9C - Simplex Algorithm: Toward Efficient...

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EE103 Lec 9C (SEJ) 1 Simplex Algorithm: Toward Efficient Computation max 4 9 7 10 0 = 6 5 123 4 3 40 4 ( ) 12 34 6 0 z xx x x x z x z T +++ + + ++ + + += 20 18 0 0 0 5 6 0, 1,. ..,6 x x z xi i + +− = ≥= 1234567 0 4971 01006 113 0104 12 20 18 40 0 0 1 0 40 aaaaaaa b T ⎡⎤ ⎢⎥ = ⎣⎦ 0 0 03 x 3 0 1 T z B B BI c == 56 02 x 2 [,] Ba a I 0 (,) ( 0 , 0 ) T B cc c 1 54 1 1 0 [, ]0 1 (0,40) 1 T z B B aa B c 1 1 1 1 1 1 1 0 1 z T B B B cB = 1 1 1 01 1 1 (2,4) 0 1 T B the pivot on B TT = EE103 Lec 9C (SEJ) 2 Simplex Algorithm: Toward Efficient Computation 0 ( ) 12 20 18 40 0 0 1 0 40 T Original data = 1 1 1 0 1 (0,40) 1 T z B B B c 1 1 1 1 1 1 1 0 1 z T B B B = 1 1 1 1 1 0 (? ) 1 T B the pivot on B w h y = 4 5 6 7 1 1 8.75 6.25 0 1 0.25 0 5 0.025 0.025 0.075 1 0 0.025 0 0.1 11 19 15 0 0 1 .75 14 3 z aaa a a a ab BT T −−
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EE103 Lec 9C (SEJ) 3 Simplex Algorithm: Toward Efficient Computation 2 14 2 [, ] , ( 1 2 , 4 0 ) T B Ba a c == 2 1 2 1 22 1 2 0 [, ]0 , 1 (12,40) 1 zz T B B aa BB cB ⎡⎤ ⎢⎥ ⎣⎦ 12 3 4 5 6 7 1 20 2 1 2.333 1.667 0 .267 .067 0 1.333 0 .033 .033 1 .007 .027 0 0.067 0 6.667 3.333 0 2.933 .267 1 18.667 z a a a a a b B T T =− = −− 1 01 : zk k Note at each iteration k BT T + = 1234567 10 : explain \\ [ , , , , , , , ] kz
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This note was uploaded on 03/30/2009 for the course EE 103 taught by Professor Vandenberghe,lieven during the Winter '08 term at UCLA.

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Lecture 9C - Simplex Algorithm: Toward Efficient...

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