fmincon stuck at an intermidiate value

Hi,fellows I am using fmincon to maximize the sum of likelihood(sumllh), which is part of a simulation. So I know the optimized value should be around 172. But it seems fmincon have worked from around more than 700 to 523 and then can't go on. It has been working more than 10 hours now. So I think there must be some problem here. Could you offer some advice I will show you the result in command window.

if true
  %sumllh =

523.2640

sumllh =

523.2640

sumllh =

523.2640

sumllh =

523.2640

sumllh =

539.0686

sumllh =

523.2640

sumllh =

523.2640

sumllh =

523.2640

sumllh =

523.2640

                                            First-order      Norm of
 Iter F-count            f(x)  Feasibility   optimality         step
    0       9   5.232640e+002   0.000e+000   2.100e+005

sumllh =

658.7498

sumllh =

705.4196

sumllh =

606.7836

sumllh =

598.1732

sumllh =

678.4877

sumllh =

713.2264

sumllh =

609.5137

sumllh =

599.1704

sumllh =

543.3757

sumllh =

545.6598

sumllh =

534.0842

sumllh =

528.5852

sumllh =

525.9029

sumllh =

524.5781

sumllh =

523.9197

sumllh =

523.5915

sumllh =

523.4276

sumllh =

523.3458

sumllh =

523.3048

sumllh =

523.2844

sumllh =

523.2742

sumllh =

523.2691

sumllh =

523.2665

sumllh =

523.2652

sumllh =

523.2646

sumllh =

523.2643

sumllh =

523.2641

sumllh =

523.2640

sumllh =

523.2640

sumllh =

523.2640

sumllh =

523.2639

sumllh =

523.2639

sumllh =

523.2640

sumllh =

523.2640

sumllh =

523.2629

sumllh =

523.2639

sumllh =

523.2639

sumllh =

523.2639

sumllh =

523.2639

    1      48   5.232639e+002   0.000e+000   6.802e+004   1.468e-010

sumllh =

523.2639

sumllh =

523.2639  end

[Walter Roberson]

Those numbers do not help us much at all. It would be easier if you were to show your code.

It seems likely that you are stuck in a local minima.

Answer 1

[Matt J]

Your function beta looks highly non-differentiable and therefore out of the scope of what fmincon can handle. You'll probably need to use ga() instead. It's also not clear how you came up with your initial guess and why you think that's close to the optimum. If you simply have no idea, all the more reason to use ga().

[Walter Roberson]

fmincon() is a local minimizer.

ga() is not certain to be able to handle the task either.

Please have a look at the Global Optimization Toolbox.

[xueqi]

Hi I tied ga. And this is the result(not the complete one since it is still running). Seems it start with a point and search a little bit and then return to the start point. What does this tell me ? Cheers!

    if true
      % sumllh =

449.1629

sumllh =

449.1629

sumllh =

449.1629

sumllh =

450.1382

sumllh =

451.8613

sumllh =

449.1629

sumllh =

449.1629

    end

[Matt Tearle]

If the function isn't smooth, you might want to try patternsearch. If it is smooth, but you're getting stuck in a local minimum, you could try GlobalSearch or MultiStart to run fmincon from multiple starting locations.

[Matt J]

Seems it start with a point and search a little bit and then return to the start point. What does this tell me ?

To me, it suggests that you have local minima almost everywhere, similar to this function,

 fplot(@(x) round(x).^2,[-4,4])

You should plot your function with respect to the different variables x(1)...x(8) to get a feel for what it looks like.

[xueqi]

The thing is the function is not smooth and also tending to stuck in a local minimum. ga and patternsearch can't be used in multistart...So how can I solve this dilemma?

[Matt J]

You don't need multistart for ga and patternsearch. They already use multiple search points internally.

[xueqi]

I find fmincon moves to the optima very fast but can't stop even it is quite near the optima. It just bounding around the optima. Some of you suggest that it is because the objective function has a singularity..And for pattersearch I have ran it for several hours now but it just improves from 417 to 415 while the optima should be around 159. I have 8 independent variables to estimate so it might make sense why it takes such a long time for pattersearch. I am even not sure what I am asking for. I just have absolutely no idea how to proceed...

[Matt J]

If you know the optimum to be around 159, don't you have enough pre-knowledge to initialize GA better than at 417?

Failing that, maybe you need a new objective function, i.e., maybe you haven't formulated the problem in the best way. It sure seems like the objective function you're working with has no nice, well behaved prooperties at all.

[xueqi]

No I can't. I know the optimum should be 159 because I am using the simulated data in this case. But when I am analyzing the experimental data, I cant know the optimum... For an different question. I have 8 independent variables for my function beta. How do I plot it with respect to each of the 8 variables?

[Matt J]

You evaluate your objective function over a range of one of your 8 unknowns while holding the other 7 fixed.