Problems with NMaximize.

• To: mathgroup at smc.vnet.net
• Subject: [mg69168] Problems with NMaximize.
• From: "Nacho" <ncc1701zzz at gmail.com>
• Date: Thu, 31 Aug 2006 04:40:03 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Hello.

I'm trying to solve a real-life problem using Mathematica and I am
having some problems with NMaximize.

As background, the problem is related to VDSL2 technology. The physical
frame can be configured using different parameters (primary parameters)
and those parameters defines the secondary parameters.

I want Mathematica to maximize the datarate in the line while
maintaining some performance on the secondary parameters.

Now, the formulas.

I want to maximize the datarate, definded as:

l*(nfec-r-1)*4000/nfec

the other constrains are:

4*d*r*i / (l*nfec) >= 4

nfec==q*i

0<= (i-1)*(d-1) / (l*500) <=0.016

And the parameters have the following restrictions:

l, nfec, r, d, i, q are all Integers (but the calculations done with
them not neccessarily).

1000<=l<=23850

1<=q<=8

1<=d<=2048

1<=nfec<=255

r can take even values between 0 and 16 (0,2,4,6,8,10,12,14,16)

I think that this is all.

I have been unable to Nmaximize the result, and as I tried different
approaches (leaving the variables as Reals and then making them
Integers little by little, eliminating some variables...) I get
different results.

Sometimes the maximized value is really low, others it fails to
converge, others it finds a 1/0 indetermination...

The best approach I could find is this one, eliminating "i" from the
equation set:

NMaximize[{l*(nfec -
r - 1)*(4000/nfec), (4*d*r)/(l*q) >= 4, 0 <= ((-1 + d)*(-1 +
nfec/q))/(500*l) <= 0.016, l â?? Integers,
nfec â?? Integers, r â?? Integers, d â?? Integers, q â?? Integers,

1000 <= l <= 23850, 1 <= q <= 8, 1 <= d <=
2048, 1 <= nfec <= 255, 0 <= r <= 16}, {l, nfec, r, d, q}]

(I hope that the E indicating that a variable belongs to a domain are
displayed). But it complains about a lot of constraints, I don't know
why...

I don't know how to say Mathematica that a variable can take just some
values (as for r being even), but I just said it is between 0 and 16.

Any help is welcomed to solve the problem.