MATLAB: Does it give me a wrong answer when I want to find the absolute minumum of the function g(t)

g= @(t)-(t.^4-10*t.^3+25*t.^2-10*t+24)

The function is

g= @(t)-(t.^4-10*t.^3+25*t.^2-10*t+24).

When I use fplot(g,[-2,7]) there I can see the minumum point is -2 in the interval. But when I use fminbnd(g,-2,7) gives me 2.0889 although I wrote fminsearch(g,1) it gives me the same point which is not right when I look the figure. When I write fplot(g,[-4,8]) there I can see that the minumum point is -4 which gives me -1360 and it is right this is the absolute minumum of the function in interval. Why can't I find the absolute minumum in interval [-2,7] which has to give me -2 but it doesn't work?

Best Answer

In general, optimizers are not capable of ensuring they have found a global optimum. If your function can be arbitrarily nasty, that can be avery difficult task. Fminbnd is pretty good. But it cannot do magic.

An optimizer will try to find a point that yields a local minimizer. It will be dependent on your starting values. So if you are not happy with the solution found, then try another start point. If you are not happy with that, then since it is your objective function, then you need to understand it better to be able to find a better start point.

Note that fminbnd does provide TWO endpoints. So you can control where it looks.

Related Solutions

MATLAB: Fminbnd finding wrong minimum point, please help

"fminbnd" gives local solutions. The curve defined by your function "f" looks like the response from an over-damped oscillator (if the mass was at equilibrium at time zero and then subsequently smacked with a hammer). So on your curve, you have local minimums at the boundaries you give to fminband (even though the function really gets smaller for greater x). Depending on where fminbnd's starting point is, it will converge to one of these solutions. In terms of the minimum being located at the defined boundaries, this is from the help menu:

The algorithm is based on golden section search and parabolic interpolation. Unless the left endpoint x1 is very close to the right endpoint x2, fminbnd never evaluates fun at the endpoints, so fun need only be defined for x in the interval x1 < x < x2. If the minimum actually occurs at x1 or x2, fminbnd returns an interior point at a distance of no more than 2*TolX from x1 or x2, where TolX is the termination tolerance.

MATLAB: Wrong Hessian output in fminunc

Another solution would be to use standalone routines for numerical gradient and hessian estimation

https://www.mathworks.com/matlabcentral/fileexchange/13490-adaptive-robust-numerical-differentiation

fun=@(x) (x(1)^2+x(2)^2);
xOpt = fminunc(fun ,[1,1]);
g=gradest(fun,xOpt)
H=hessian(fun,xOpt)

No hidden scale factors if you go that route:

xOpt =
     0     0
g =
     0     0
H =
    2.0000         0
         0    2.0000

Best Answer

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MATLAB: Fminbnd finding wrong minimum point, please help

MATLAB: Wrong Hessian output in fminunc

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