Originally posted by: jamedadi

Hello

I have faced a non-linear problem in my modeling. My model is as follows:
max sigma {x_i}
s.t.
x_i.y_i=z_i 1<i<n
....
some linear constrains

In this models, x_i, y_i, and z_i are continuous variables for {1<i<n}. As you can see we have a product term in constrains. My question is if this problem is P or NP? I strongly think it is NP. This is because the I found that the product term can be approximated by peicewise linear optimization techniques ("AIMMS Optimization Modeling" ebook, chapter 7, http://www.aimms.com/downloads/manuals/optimization-modeling ). This method convert the constrain to a MILP form, which is NP-hard. But this proof is not precise. So, I would like to ask if anyone can help me on this topic.

Thanks
#DecisionOptimization
#MathematicalProgramming-General