  In an interference network, joint power and admission control aims to support
a maximum number of links at their specified signal to interference plus noise
ratio (SINR) targets while using a minimum total transmission power. In our
previous work, we formulated the joint control problem as a sparse
$\ell_0$-minimization problem and relaxed it to a $\ell_1$-minimization
problem. In this work, we propose to approximate the $\ell_0$-optimization
problem to a p norm minimization problem where $0<p<1$, since intuitively p
norm will approximate 0 norm better than 1 norm. We first show that the
$\ell_p$-minimization problem is strongly NP-hard and then derive a
reformulation of it such that the well developed interior-point algorithms can
be applied to solve it. The solution to the $\ell_p$-minimization problem can
efficiently guide the link's removals (deflation). Numerical simulations show
the proposed heuristic outperforms the existing algorithms.
