- #1
brydustin
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I know by default that Mathematica will use the BFGS method when you request "FindMinimum[Function]" but I am curious for a hint towards a pseudo-code for the following problem:
I have a collection of functions, say F = {f1,f2,...,fN} and I want to transform them as linear combinations of one another i.e.
fJ' = a(f1) + b(f2) + ... + c(fi) + d(fJ) + ... + n(fN) such that the transformed set, say
F' = {f1',f2',...,fN'} optimizes a function B(f1,f2,...,fN).
Now, this makes B, strictly speaking, a function of the mixing coefficients (a,b,...c,...,n)_J
(that is to say, for each fJ, the transformed fJ' has its own mixing coefficients). If we put these in a matrix and act them on F, we get F' (and the matrix has N*N components).
How may I apply the BFGS algorithm (its already built in Mathematica), so that I can get these coefficients (notice the Hessian is taking the partials of B with respect to the coefficients which mix f1,...fN, and the f's are actually "fixed"/i.e. given)
I have a collection of functions, say F = {f1,f2,...,fN} and I want to transform them as linear combinations of one another i.e.
fJ' = a(f1) + b(f2) + ... + c(fi) + d(fJ) + ... + n(fN) such that the transformed set, say
F' = {f1',f2',...,fN'} optimizes a function B(f1,f2,...,fN).
Now, this makes B, strictly speaking, a function of the mixing coefficients (a,b,...c,...,n)_J
(that is to say, for each fJ, the transformed fJ' has its own mixing coefficients). If we put these in a matrix and act them on F, we get F' (and the matrix has N*N components).
How may I apply the BFGS algorithm (its already built in Mathematica), so that I can get these coefficients (notice the Hessian is taking the partials of B with respect to the coefficients which mix f1,...fN, and the f's are actually "fixed"/i.e. given)
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