  In this paper, we consider a class of sparse regression problems, whose
objective function is the summation of a convex loss function and a cardinality
penalty. By constructing a smoothing function for the cardinality function, we
propose a projected neural network and design a correction method for solving
this problem. The solution of the proposed neural network is unique, global
existent, bounded and globally Lipschitz continuous. Besides, we prove that all
accumulation points of the proposed neural network have a common support set
and a unified lower bound for the nonzero entries. Combining the proposed
neural network with the correction method, any corrected accumulation point is
a local minimizer of the considered sparse regression problem. Moreover, we
analyze the equivalent relationship on the local minimizers between the
considered sparse regression problem and another regression sparse problem.
Finally, some numerical experiments are provided to show the efficiency of the
proposed neural networks in solving some sparse regression problems in
practice.
