Minimize a function in matlab where the variable of the function is a vector in R^n

Question

I have to minimize transpose(x)*A*x ./ transpose(x)*B*x function where x is a vector, A and B are matrices. Is there a function in matlab that will minimize it?

Thanks

Answer 1

If you have a multivariate scalar function (which it appears you have) you can use fminunc, referred to here.

Also, I take it you are trying to perform (x'Ax)/(x'Bx) <-- the apostrophe is transpose in MATLAB.

Here's an example:

>> A = rand(3)

A =

0.8491    0.7577    0.6555
0.9340    0.7431    0.1712
0.6787    0.3922    0.7060

>> B = rand(3)

B =

0.0318    0.0971    0.3171
0.2769    0.8235    0.9502
0.0462    0.6948    0.0344

>> f = @(x)x'*A*x./(x'*B*x);
>> fminunc(f,[1;2;4]) % some arbitrary starting guess.
Warning: Gradient must be provided for trust-region algorithm; using quasi-newton algorithm instead. 
> In fminunc at 403 

Local minimum found.

Optimization completed because the size of the gradient is less than the default value of the function tolerance.

<stopping criteria details>


ans =

-7.3912
 2.1750
 5.5588

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