Optimization of a matrix with an objective function (for ML) - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-26T09:37:40Z http://mathoverflow.net/feeds/question/85325 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/85325/optimization-of-a-matrix-with-an-objective-function-for-ml Optimization of a matrix with an objective function (for ML) id0 2012-01-10T10:50:53Z 2012-01-10T11:36:26Z <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>