Consider the L0 norm compressed sensing problem:
$$\eqalign{ & \min \quad {x^T}Qx + {c^T}x + {\mu\left\| x \right\|_0} \cr & s.t:\quad Ax \le b \cr} $$
Suppose I do want to solve this problem as is (or use the best possible heuristics available) using state of the art software like Gurobi instead of doing L1 norm approximation. How should I reformulate the problem to achieve best results practically? I know that I could perform do the big M formulation though in MIQP, is it the best we could do in terms of practice (I could tolerate inexact/"almost optimally practically" solutions)?
