  In this paper we propose and study a family of sparsity-inducing penalty
functions. Since the penalty functions are related to the kinetic energy in
special relativity, we call them \emph{kinetic energy plus} (KEP) functions. We
construct the KEP function by using the concave conjugate of a
$\chi^2$-distance function and present several novel insights into the KEP
function with $q=1$. In particular, we derive a thresholding operator based on
the KEP function, and prove its mathematical properties and asymptotic
properties in sparsity modeling. Moreover, we show that a coordinate descent
algorithm is especially appropriate for the KEP function. Additionally, we
discuss the relationship of KEP with the penalty functions $\ell_{1/2}$ and
MCP. The theoretical and empirical analysis validates that the KEP function is
effective and efficient in high-dimensional data modeling.
