How to speed up fmincon?

Hello, I'm trying to get optimized two parameters in the differential equations. I've already gotten very helpful answers when I asked here using a simple example. So now I know how to make my code, but my actual system is consisted of 64 differential equations. In other words, my goal is to find out two parameters that are in all differential equations, while solving 64 differential equations to make one objective function to minimum. But when I run the code, it was running for several hours. And it's still 'busy'. Does that mean my code has a problem? I'm attaching my code. Please help me. Thank you.

Answer 1

[Matt J]

Your tolerances 'TolX',1e-100,'TolCon',1e-100 are extremely small. That can protract the optimization.

[Matt J]

Since it's just nonlinear least squares with bound constraints, it would also make more sense to use lsqnonlin. That could be faster than fmincon, since it is more specialized.

At minimum, do not use AA,b inputs to specify simple bound constraints. Use the lb,ub arguments.

[kkng]

Thank you for your comment. The reason why I reduce both is that when I ran the code with default TolX and TolCon, it gave me the message below after ~ 50 min.

fmincon stopped because the size of the current step is less than the default value of the step size tolerance and constraints were satisfied to within the default value of the constraint tolerance.

criteria details

ans =

   14.0000
   20.0000

But this results are not right. They are just initial values. So I tried to decrease them. If those changes make a problem, what can I do now? Any help would be appreciated.

[Matt J]

Replacing AA,b constraint data with ub,lb data could also speed things up. What is the time per iteration that you are seeing?

[kkng]

Thank you, Matt. I didn't know how to see the iteration status. Now, I change AA and b to ub and lb, and use algorithm with 'sqp'. Also, 'TolX, and 'TolCon' are back to default values. Then it took about several mins for one iteration. I don't know it's reasonable time or not. Is there any way to reduce change step for parameters within boundaries? For example, one of my parameter has lb=20 and ub=35. Then Matlab varies it within this range starting from 20. (initial guess is 20). I'm wondering how much it is changed after start. Can I change it? Thank you!

[Matt J]

The amount by which the parameters change are all inter-related and depend on the current value of the parameter vector x. I'm not sure what you hope to gain by changing it.

If the time per iteration is several minutes, I think you're going to be stuck with hours long optimization times, unless you have a very good initial guess.

[kkng]

Thank you again for your comment. You're right. I got the different result when I put the different initial guesses. To reduce the iteration time, I tried ode15s instead of ode113, but the error message was appeared during nonlinearsquare.m. Attempted to access y(24,64); index out of bounds because size(y)=[23,64]

I also tried to solve my 64 differential equations with fixed parameters as a test. It turned out that ode 113 and ode15s gave me the different number. I was surprised that they didn't give the same result. (I'm a beginner in Matlab.) I'm still stuck in the problem. Can I try anything else? Thank you!!!!

[Marc]

First off it should not surprise you that two different ODE integrators give you different results.

Second, when optimizing odes like this, you should first off try to "optimize" which ode integrator to use by timing the solution to the ode equation. If it takes ode15s 0.1s to solve your system, expect the optimization to take awhile. Since you are only looking at two parameters, a quick sensitivity analysis of time vs ode integrator, along with "accuracy" should be easy.

Now back to your problem... Try fminsearch. I have found that the nelder mead simplex routines which do not rely on jacobians or hessians to be more robust to these kinds of systems.

Be careful how you are defining your objective function. Scaling this could be of help.