A multiple linear regression is to use several predictor variables to predict the outcome of a response variable, like the following relationship:
$y_{i}=\beta_{1}x_{i1}+...+\beta_{p}x_{ip}+\epsilon_{i}, i=1,...,n$
I understand the typical objective to learn the $\beta$ paramters is least-squares, which means to minimize the sum of the sqaure of $\epsilon_{i}$. Now I want other kinds of objective, for example to maximize the Shannon entropy of the sequences of $\epsilon$ (or other self-specified objective). I googled towards this direction but no luck. I am wondering if there is any problem (and tool to solve it if possible) I can look into to do that?
Thank you for your help.