Tuesday, February 21, 2012

max tricks

The following condition

image

can be easily written as

image

 

However when we have:

image

 

then we need more sophistication. Something like:

image

Here we introduced a variable y that assumes the value of the maximum of the x’s. The following expression will give a good big-M value:

image

See also: http://orinanobworld.blogspot.com/2012/01/maxmin-bounds.html

A slightly more direct formulation would be:

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If we are really want to show off, we can only generate this if

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and use the simpler adjustment of bounds

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otherwise.