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01/30/07 4:58pm

Hi all,

I'm running some complicated nonlinear problems. Most of the terms constituting the objective function and constraints are
1. Square roots of 2 variables - Sqrt[b[i]^2-b[i-1]^2]
2. Simple squares c*b[i]^2.
3. "Linear members" - c*b[i]

Number of variables shouldn't exceed 50. I ran NMinimize with default settings. For less than 10 variables it usually takes less then 2 hours to solve. For a very small number (<5) it's a matter of minutes actually. For more then 10 variables it takes between 1 and 3 days. For 14 and 15 variables Mathematica reports this:

"No more memory available.
Mathematica kernel has shut down.
Try quitting other applications and then retry."

I'm looking at steps to make Mathematica run faster.
1. Could anyone suggest what Method to use:
NelderMead, DifferentialEvolution...
2.What would be a vise guess for the method options, taking into account the nature of constraints and obj function.
3. We have used default numerical settings (precission,...) too.
4.Oh yeah, I'm running iMac.
5. Does anyone have experience with Mathematica compiler and how much it improves performance in similar situations. Should I expect good things from it?
6. Has anyone experienced a similar "not enough memory" error?

I apologize for asking dumb questions about numerical methods. I do not know anything about them. To me it is just a means of solving a problem not a research area.

Thanks a lot!

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