Why does my optimization stop after the first iteration?

I do not know much about numerical optimization. My question is, what are possible reasons for fmincon to stop after 0 iterations. Here are the clues:

• I do not provide a gradient or hessian.
• It stops because:"size of the current step is less thanthe default value of the step size tolerance and constraints are satisfied to within the default value of the constraint tolerance"
• feasibility is 0.0000,First-order optimality is 1.206e+09
• Using patternsearch works and it finds the optimum

Another question: I suspect, that patternsearch is much slower than fmincon when the number of arguments increases, right?

Thank you for your time.

[jgg]

It stops because the default tolerances are met and the step size is small enough. You'll have to adjust these to get it to perform better.

A more fundamental point is that fmincon is a local optimizer; if you start near a locally flat point, it will just stop at the flat point. Patternsearch is a global optimizer and should perform better.

I'm not sure about the time comparisons between the two algorithms; I'd guess you're right, but it's probably not a huge difference when you don't provide a gradient to fmincon.

[Rosi Marungu]

Thank you for your answer. Some follow up questions: Isn't it odd that it stops even though First-order optimality is 1.206e+09? This should be a number as small as possible, right? So shouldn't there be a threshold above which the solver cannot declare to have found a solution?

Does that give a clue about what the function looks like at that point?

Thank you very much.

[Matt J]

This should be a number as small as possible, right?

First order optimality isn't the only criterion that can trigger a stop. Also, to be considered small, a value for the first-order optimality measure need only be small relative to typical magnitudes of the function's derivative. Try this simple problem, for instance,

 [x,fval,ef,out]=fmincon(@(x) 1e18*x^2,.5,[],[],[],[],0,1)

You will see that out.firstorderopt is ~1e9.

Bottom line -- we really need to see your code.