The following picture illustrates the problem:
The blue line is what we want to model:
y={0if 0≤x≤a(x−a)Hb−aif a<x<bHif x≥b |
Is there much we can exploit here, from this simple structure? I don’t believe so, and came up with:
x1≤aδ1aδ2≤x2≤bδ2bδ3≤x3≤Uδ3δ1+δ2+δ3=1x=x1+x2+x3y=(x2−aδ2)Hb−a+Hδ3δk∈{0,1}xi≥00≤x≤U |
Update
Added missing ∑kδk=1, see comments below.
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