# Implementing a regularization term in ridge regrssion

I am trying to solve the ridge regression problem given by

$$D_{s} = min_{D_{s}} \hspace{2mm} || X_{s} - D_{s}Y_{s}||_F^{2} + \lambda \hspace{2mm} ||D_{s}||_{F}^{2} \hspace{10mm} s.t. \hspace{5mm} ||d_{i}||_{2}^{2} \leq 1$$

What extra information is this $$||d_{i}||_{2}^{2} \leq 1$$ giving and how to incorporate this in the objective function.

Actually, I tried to incorporate $$||d_{i}||_{2}^{2} \leq 1$$ by writing it as $$||D_{s}||_{F}^{2} \leq 1$$. Am I correct ?

$$D_{s}$$ is the matrix that need to be learnt.

• Could you clarify your notation and the type of problem you are addressing? It looks like a multivariate regression model where you have more than one dependent variable for each observation. However using the standard notation of $Y$ for the dependent variables and $X$ for the independent variables, then your sum of squared errors would be $\|Y-XD\|$ instead of $\|X-YD\|$. Also could you clarify if $d_i$ is a row or column of $D_s$? Finally, presumably the constraint is supposed to hold for all $i$. Commented Mar 4, 2020 at 14:29