On the Smoothing of the Norm Objective Penalty Function for Two-Cardinality Sparse Constrained Optimization Problems

Abstract This paper studies a smoothing norm objective penalty function for two-cardinality sparse constrained optimization problems. Good properties are proved for the smoothing norm objective penalty functions in solving two-cardinality sparse constrained optimization problems, after which an algorithm is presented. Furthermore, its convergence is also proved under some conditions. The proposed algorithm can solve a satisfactory approximate optimal solution in a numerical example.