I wonder if there some existing work of Linear Regression or Logistic Regression with partially known coefficients ($\beta$).
For a linear regression, $Y=X\beta$, when we already have knowledge about some coefficient of $\beta$, say $\beta_{0,...,j}$ and still need to solve for $\beta_{j,..., p}$.
This should be trivial for linear regression case since we can directly deduct the known part out of $Y$, but how about Logistic Regression?
And what if we don't know the actual values of $\beta_{0,...,j}$, but only know that they should be non-zero.
I believe these could be solved with some constrained optimization, so my question is that if there are some published manuscripts that have studied this problem? I wonder because I am interested in whether there are some interesting theoretical aspects of this more than a constrained optimization problem.