I have the following quadratic program: Minimize $b^Tb$ subject to $Ax=b$ where $A$ is a $n\times m$ matrix ($n\leq m$) of rank $n-1$. I also want $0\leq x\leq 1$.
For my choice of $A$, I can prove that the minimizer vector $b$ is unique, however obviously the vector $x$ cannot be unique because of the rank of $A$. I am trying to find the $b$ value I want (I don't really care about the $x$), and so ideally, I would like to write my quadratic program in the equivalent form:
Minimize $b^Tb$ subject to $Zb \leq r$ for some appropriate matrix $Z$ and vector $r$ with no dependency on $x$. Is this possible?