I am a new learner of optimization, and I am confused by the question below, (how to change a 0-norm constrain into binary and linear constrain ?)
Given a sparse data fitting problem:
$ minimize \quad \| Ax-b \|^{2}_{2}$
$ s.t. \qquad \|x\|_{0} \le K, $
$x \in R^{n}$
Suppose we are given a constant $M > 0$ such that $\|x^{*}\|_{\infty} \le M$ for some optimal solution $x^{*}$ to this problem. How can we paraphrase this problem with only linear and binary constraints?
Thanks for any help.