piecewise linear in NLP

[Anh The]

dear all,

I have question about piecewise linear approximation,
i have parameters x,y in tables (example  x = {1,2,3,4,5,6,7}, and parameter y = {2,3,5,7,9,10,12}). How that nonlinear  term can be approximated by piecewise linear in LP or NLP (not use MIP)

Thank you in advance,

Anh The

[Marcel Hunting]

Hi,

It is not clear to me to which nonlinear term you are referring; you
do not mention any variables.

Do you mean that you have some variable v that you want to be
piecewise linear with v(1)=2, v(2)=3, v(3)=5, etc? Chapter 7 of the
AIMMS Optimization Modeling book explains how to model a piecewise
linear function. In general you need binary variables to model this.
Why don’t you want to use MIP?

Marcel Hunting
AIMMS Software Developer

[Anh The]

Dear Marcel Hunting,

I have used MIP to model piecewise linear, but for a large model, the execution time increases quickly.
Can you have method to model piecewise linear in NLP.?

Best regards,

Anh The

2011/8/10 Marcel Hunting <Marcel....@aimms.com>

Hi

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[Marcel Hunting]

Hi,

If you want to add piecewise linear functions to a NLP problem then
normally you have to use binary variables and you end up with a MINLP
problem (which can be more difficult to solve).

In theory you can model a binary variable x by giving it a continuous
range [0,1] and adding the nonlinear constraint x^2 = x (which is only
true for x=0 and x=1) but I doubt NLP solvers can handle many of those
“binary” variables efficiently.

Marcel Hunting
AIMMS Software Developer

On Aug 11, 3:40 am, Anh The <anhthe...@gmail.com> wrote:
> Dear Marcel Hunting,
>
> I have used MIP to model piecewise linear, but for a large model, the
> execution time increases quickly.
> Can you have method to model piecewise linear in NLP.?
>
> Best regards,
>
> Anh The
>

> 2011/8/10 Marcel Hunting <Marcel.Hunt...@aimms.com>

> >http://groups.google.com/group/aimms?hl=en.- Hide quoted text -
>
> - Show quoted text -

[Anh The]

Thank you very much for the respond.

Best regards

2011/8/11 Marcel Hunting <Marcel....@aimms.com>