A Smoothing Penalty Function Algorithm for Two-Cardinality Sparse Constrained Optimization Problems

In this paper, a smoothing penalty function for two-cardinality sparse constrained optimization problems is presented. The paper proves that this type of the smoothing penalty functions has good properties in helping to solve two-cardinality sparse constrained optimization problems. Moreover, based on the penalty function, an algorithm is presented to solve the two-cardinality sparse constrained optimization problems, with its convergence under some conditions proved. A numerical experiment shows that a satisfactory approximate optimal solution can be obtained by the proposed algorithm.