[] Machine learning constrained linear regression

Consider a linear regression model:
$y=X\beta+\varepsilon$ where $\varepsilon$ for the residuals of the model. In the linear regression model with no constraints, we use the least squares method, hope and minimum residual sum of squares. which is $min (\ sum [(yX \ beta)] ^ 2)$

On this basis, plus a set of linear constraints:

written in matrix form:
$R \ beta = q$

Linear regression problem with constraint can be described as follows:

$min (\ sum [(yX \ beta)] ^ 2)$
$s.t.R\beta=q$
using Lagrange multiplier method:

for $\beta,\lambda$ derivative, after a series of calculations, resulting $\beta^*$ And $\lambda$ are as follows:
$\beta^*=\beta-(X'X)^{-1}R'[R(X'X)^{-1}R']^{-1}(R\beta-q)$
$\lambda=[R(X'X)^{-1}R']^{-1}(R\beta-q)$
wherein $\beta$ is a parameter value without constraint.