Optimization of a matrix with an objective function (for ML) - MathOverflow most recent 30 from http://mathoverflow.net2013-05-26T09:37:40Zhttp://mathoverflow.net/feeds/question/85325http://www.creativecommons.org/licenses/by-nc/2.5/rdfhttp://mathoverflow.net/questions/85325/optimization-of-a-matrix-with-an-objective-function-for-mlOptimization of a matrix with an objective function (for ML)id02012-01-10T10:50:53Z2012-01-10T11:36:26Z
<p>Hi.</p>
<p>I need to do max. likelihood for an objective likelihood function L (minimize it), and the target is a matrix. ie:</p>
<p>$$min_KL(K)$$ </p>
<p>For example:
K is, let's say, of size 3x3 and with initial value of ones ($k_{i,j}=1∀i,j$).
L is $L=∥\nabla(K)∥$ or $L=∥K∥^{1.1}$.</p>
<p>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:
$K:=K-f(\nabla(L))$, but I don't know what.</p>
<p>*note: It might have something to do with the Euler-Largange method ($L_x-L_t\left(L_{x'}\right)=0$) but I'd have to do it iteratively if any...</p>
<p>Appreciate any help.</p>