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matlabfunctionfminsearch

Use fminsearch to find local minimizer and the minima at that value

I am having trouble using fminsearch: getting the error that there were not enough input arguments for my function.

f = @(x1,x2,x3) x1.^2 + 3.*x2.^2 + 4.*x3.^2 - 2.*x1.*x2 + 5.*x1 + 3.*x2 + 2.*x3;
[x, val] = fminsearch(f,0)

Is there something wrong with my function? I keep getting errors anytime I want to use it as an input function with any other command.

Solution

  • I am having trouble using fminsearch [...]

    Stop right there and think some more about the function you're trying to minimize.

    Numerical optimization (which is what fminsearch does) is unnecessary, here. Your function is a quadratic function of vector x; in other words, its value at x can be expressed as

    x^T A x + b^T x

    where matrix A and vector b are defined as follows (using MATLAB notation):

    A = [ 1 -1 0;
     -1  3 0;
      0  0 4]

    and

    b = [5 3 2].'

    Because A is positive definite, your function has one and only one minimum, which can be computed in MATLAB with

    x_sol = -0.5 * A \ b;

    Now, if you're curious about the cause of the error you ran into, have a look at fuesika's answer; but do without fminsearch whenever you can.