# Minimize function with respect to multiple variables

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Nick Klodowski
on 10 Nov 2011

Commented: Walter Roberson
on 3 Apr 2019

Hi,

I have a function f(b1,b2,b3,x,y1,y2,y3) that requires multiple inputs. How can I find the values of b1, b2, and b3 that minimize this function for given values of x, y1, y2, and y3?

Thanks for the help.

##### 0 Comments

### Accepted Answer

Jonathan
on 10 Nov 2011

You can use the function fminsearch for this, which requires an initial guess. Here is how it might look for you.

x = 1;

y1 = 2;

y2 = 3;

y3 = 4;

fun = @(b) f(b(1), b(2), b(3), x, y1, y2, y3);

b_guess = [10 20 30];

b_min = fminsearch(fun, b_guess);

b1_min = b_min(1);

b2_min = b_min(2);

b2_min = b_min(3);

Let me know if this answers your question.

~Jonathan

##### 8 Comments

Vignesh
on 3 Apr 2019

Walter Roberson
on 3 Apr 2019

### More Answers (1)

Mohamad Alsioufi
on 9 Dec 2017

Edited: Mohamad Alsioufi
on 9 Dec 2017

Hi there, I have the same problem, but when I tried to use 'fminsearch' function I had some problems, the following code is a part of my function myGP(x,y,x_star,y_hat):

segmaSE = 1;

lengthSE = 1;

theta0 =[segmaSE lengthSE];

kernelFunc = @(x1,x2,theta)(theta(1)^2)*exp(-0.5*(pdist2(x1/theta(2), x2/theta(2)).^2));

marginal_likelihood =@(y,x,theta,N) -0.5*y'*pinv(kernelFunc(x,x,theta))*y - 0.5*log(abs(kernelFunc(x,x,theta))) - N*.5 * log (2*pi);

fun = @(theta)marginal_likelihood(y,x,theta,N);

theta0 =[segmaSE lengthSE];

theta=fminsearch(fun,theta0);

However I got the following error:

Assignment has more non-singleton rhs dimensions than non-singleton subscripts

Error in fminsearch (line 200) fv(:,1) = funfcn(x,varargin{:});

Error in myGP (line 21) theta=fminsearch(fun,theta0);

Any idea about this error?

##### 1 Comment

Walter Roberson
on 9 Dec 2017

You do not give us any information about the sizes of the variables, which makes it difficult to test.

I notice that you always call kernelFunc() with (x, x, theta). If x is scalar or row vector then the result of the pdist2() call will be 0. If x is N x M for N > 1 then the result of the pdist2() will be N x N. The exp() will not change that, and multiplying by the scalar will not change that.

pinv() of N x N will be N x N . In order for pinv()*y to work, y must be N x P for some P, with the * giving an N x P result. The y' * before that would be * of a P x N, so that would be P x N * N * P, giving a P x P result. You multiply that by -0.5 and you subtract 0.5*log(abs(kernelFunc(x,x,theta))) where we have already determined that the kernelFunc returns an N x N result. P x P minus N x N will work under the circumstance that P is 1 or P is N; either way the subtraction going to return a N x N result .

Now, the objective function return value for fminsearch needs to be a scalar. For N x N to be scalar, then x would have had to have been N x M = 1 x M -- but in that case the pdist2() would return 0 making it essentially useless to make the pdist2() call.

This suggests that your formula is either fundamentally incorrect (but it does not look to be wrong), or else that you are asking for a matrix minimization, which fminsearch() cannot handle.

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