I would like to solve a homogeneous least squares problem (i.e. a linear least squares problem where the constants are all zero but where I want to avoid the trivial zero solution). The usual form of these problems:
$\min_{\bf x} \|{\bf Ax}\|$, s.t. $\|{\bf x}\|=1$
can be solved by taking the SVD of ${\bf A}$ and the solution is given by the last column of the matrix ${\bf V}$ from the SVD. However, I am interested in solving a constrained version of this problem, namely:
$\min_{\bf x} \|{\bf Ax}\|$, s.t. $\|{\bf x}\|=1$ and ${\bf Bx}\geq 0$
Is there a closed form solution to this problem?