Issues with implementing Newton's method for optimization

Issues with implementing Newton's method for optimization

I have this function $f(\mathrm{X})$ where $\mathrm{X}$ is a positive
definite matrix. I am trying to optimize this function using Newton's
method. So at any point $\mathrm{X}$', I will make a quadratic
approximation using Taylor's series and minimize the quadratic. However, I
want to impose some of the elements of $f(\mathrm{X})$ to be $0$, that
means they are constant $0$. How can I do this in Newton's method. Further
to get the descent direction how can I impose these constraints because
when I try to find the descend direction to minimize the quadratic, I
might have to make the coefficients to be zero to be non zero. How can I
enforce these constraints?