13.4: fminsearch

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The fminsearch function is similar to fzero, which we saw in Chapter 7. Recall that fzero takes a function handle and an initial guess, and it returns a root of the function. As an example, to find a root of the function

function res = error_func(x)
    res = x^2 - 2;
end

we can call fzero like this:

>> x = fzero(@error_func, 1)
ans = 1.4142

The result is near the square root of 2. Let’s call fminsearch with the same function:

>> x = fminsearch(@error_func, 1)
x = -8.8818e-16

The result is close to 0, which is where this function is minimized. Optionally, fminsearch returns two values:

>> [x, fval] = fminsearch(@error_func, 1)
x = -8.8818e-16

fval = -2

The x is the location of the minimum, and fval is the value of the function evaluated at x.

If we want to find the maximum of a function, rather than the minimum, we can still use fminsearch by writing a short function that negates the function we want to maximize. In the baseball example, the function we want to maximize is baseball_range; we can wrap it in another function like this:

function res = min_func(angle)
    res = -baseball_range(angle);
end

And then we call fminsearch like this:

>> [x, fval] = fminsearch(@min_func, pi/4)

x = 0.6921

fval = -131.5851

The optimal launch angle for the baseball is 0.69 rad; launched at that angle, the ball travels almost 132 m.

If you’re curious about how fminsearch works, see “How fminsearch Works” on page 15.3.