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I need to do max. likelihood for an objective likelihood function L (minimize it), and the target is a matrix. ie:

[tex]min_{K}\,\, L(K)[/tex]

For example:

K is, let's say, of size 3x3 and with initial value of ones. ([tex]k_{i,j}=1\forall i,j[/tex])

L is [tex]L=\Vert grad(K) \Vert[/tex] or [tex]L=\Vert K \Vert^{1.1}[/tex].

I know how to do gradient descend etc., but here I need to minimize the function L by iterating over K and I don't really know how to approach it. I'd expect something of this sort:

[tex]K\,:=\,K+f(grad(L))[/tex], but I don't know what.

Appreciate any help.

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# Optimization of a matrix with an objective function (for ML)

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