how to find minimumvalue in discontinuous function??

In this function,

absohandle=@(t)-abs(exp(t).*(1.0./2.0)-2.0)

I want to find minimum function value in the range 0<=t<=2.... so i used fminbnd like this.

[minimumposition, minimumfunctionvalue]=fminbnd(absohandle,0,2)

But the result is false.

In matlab's result is minimumposition=4.8379e-05 minimumfunctionvalue=-1.5000

but the true result is minimumposition=2 minimumfunctionvalue=-1.6945

In this situation, how to modify my code???

Answer 1

[Cam Salzberger]

Hello Seong,

If you check the documentation for fminbnd, it says that it only looks for a local minimum. It can't guarantee that this is the correct global minimum across the boundary.

On the other hand, the Global Optimization Toolbox is made for finding the global solution instead of local solutions. Since this is a simple 1-D problem, you can easily solve it with a GlobalSearch object, simply following the example on the doc page.

problem = createOptimProblem('fmincon', ...
    'objective', absohandle, ...
    'x0', 1, 'lb', 0, 'ub', 2);
gs = GlobalSearch;
[x, f] = run(gs, problem)

Alternatively, you could iterate over the range in small increments with fminbnd, then pick the lowest point out of those results. Or do an initial spread of a 100 points or something and calculate the values, picking the bounds based on the lowest points discovered there. But global optimization methods are far more likely to produce the correct result.

-Cam

[Seong Ik Kim]

Thank you for your answer!! From now on i didn't read docu entirely. And i don't know globalsearch..... Again, Thank you...