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Thursday, May 18, 2017

Simple piecewise linear problem, not so easy with binary variables

The following picture illustrates the problem:

image

The blue line is what we want to model:

y={0if 0xa(xa)Hbaif a<x<bHif xb
 

Is there much we can exploit here, from this simple structure? I don’t believe so, and came up with:

x1aδ1aδ2x2bδ2bδ3x3Uδ3δ1+δ2+δ3=1x=x1+x2+x3y=(x2aδ2)Hba+Hδ3δk{0,1}xi00xU
Update

Added missing kδk=1, see comments below.

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