Optimization of multivariable function using fminunc

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편집: Walter Roberson 2015년 6월 11일
Hi, I have a function of the form H = X*matrix(A) + Y*matrix(B) and matrix(A) and (B) are fixed. I need to optimize X and Y simultaneously, how can I do it?
For example: if I just had H=X*matrix(A) + matrix(B), I could have used fminunc. I could have created a function handle for H and pass it as an argument in fminunc. I know how to do it for single variable, but I just don't know how to do it in multiple variable. I looked up many resources, including many old post, but I got more confused. Any help would be appreciated. Thank You
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Walter Roberson 2015년 6월 10일
are X and Y matrices or vectors? If they are matrices then H is a matrix, and in that case you need to define what it means to "optimize" H. Lowest trace? Smallest sum-of-squares?

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답변(1개)

Drew Davis 2015년 6월 10일
Define your function handle like so:
f = @(x) x(1:a) * A + x(a+1:end) * B
where:
X = x(1:a) , Y = x(a+1:end)
then
x = fminunc(f , x0);
where:
X0 = x0(1:a) , Y0 = x0(a+1:end)
Note 'a' is the number of elements in the 'X' vector.
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Walter Roberson 2015년 6월 11일
Okay, but we still end up with problems with the output size. The only non-trivial case of this form that fminunc can deal with has a trivial solution of letting some of the components go to infinity or negative infinity. This then gets back to the question I posed earlier about what about the matrix is to be "minimized", such as possibly the trace.

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