fminbnd — Find a local minimum of a scalar function on a bounded interval using Brent's method.

x = fminbnd(fun, x1, x2) searches the closed interval [x1, x2] for a local minimum of the scalar function fun using Brent's method (golden-section search combined with parabolic interpolation). Additional output arities expose the function value at the minimum, an exit flag, and a diagnostic struct.

How fminbnd works

• The function handle must return a finite real scalar for every sampled point in the interval.
• If x1 > x2, the bounds are inconsistent and exitflag = -2.
• If x1 == x2, that point is returned with exitflag = 1.
• Options are supplied as a struct, usually built with optimset. TolX, MaxIter, MaxFunEvals, and Display are accepted.
• Display may be 'off', 'iter', 'notify' (default; only prints when the solver fails to converge), or 'final'.
• exitflag is 1 on convergence within TolX, 0 when the iteration or evaluation budget is exhausted.
• The fourth output is a struct with iterations, funcCount, algorithm, and message fields.

Examples

Minimize a quadratic

x = fminbnd(@(x) (x-2).^2, 0, 5)

Expected output:

x =
    2.0000

Capture the function value too

[x, fval] = fminbnd(@(x) (x-3).^2 + 1, 0, 5)

Expected output:

x =
    3.0000
fval =
    1.0000

Tighten tolerances

opts = optimset('TolX', 1e-10, 'Display', 'off');
[x, fval, exitflag] = fminbnd(@cos, 0, pi, opts)

Expected output:

x =
    3.1416
fval =
   -1.0000
exitflag =
     1

FAQ

Related Math functions

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how fminbnd works, line by line, in Rust.

• View fminbnd.rs on GitHub
• Learn how the runtime works
• Found a bug? Open an issue with a minimal reproduction.

About RunMat

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