MIE376 Lec 3 - Revised Simplex.page5

MIE376 Lec 3 - Revised Simplex.page5 - − − − − −...

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MIE376 Mathematical Programming Lecture Notes Daniel Frances © 2011 5 = = = 2 / 5 2 / 9 7 16 2 / 3 2 / 1 2 / 1 2 / 1 1 b B x B and ( ) ! ! ! 2 / 23 2 / 5 2 / 9 1 2 = = = B T B x c z Why the name Product Form of the Inverse? Suppose an LP has five iterations and in the last iteration we calculate 1 4 1 5 1 5 = B E B . Then we can also express this inverse as 1 1 1 2 1 3 1 4 1 5 1 0 1 1 1 2 1 3 1 4 1 5 1 1 1 2 1 3 1 4 1 5 1 2 1 3 1 4 1 5 1 3 1 4 1 5 1 4 1 5 1 5
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Unformatted text preview: − − − − − − − − − − − − − − − − − − − − − − = = = = = = E E E E E B E E E E E B E E E E B E E E B E E B E B Thus an inverse can be expressed as a product of E matrices which are easily invertible, and can easily be multiplied as all but one column are unit columns....
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This note was uploaded on 07/10/2011 for the course MIE 376 taught by Professor Daniel during the Spring '11 term at University of Toronto.

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