CONVERGENCE PROPERTIES OF STOCHASTIC PROXIMAL SUBGRADIENT METHOD IN SOLVING A CLASS OF COMPOSITE OPTIMIZATION PROBLEMS WITH CARDINALITY REGULARIZER

. In this paper, we study a class of composite optimization problems, whose objective function is the summation of a bunch of nonsmooth nonconvex loss functions and a cardinality regularizer. Firstly we investigate the optimality condition of these problems and then suggest a stochastic proximal subgradient method (SPSG) to solve them. Then we establish the almost surely subsequence convergence of SPSG under mild assumptions. We emphasize that these assumptions are satisfied by a wide range of problems arising from training neural networks. Furthermore, we conduct preliminary numerical experiments to demonstrate the effectiveness and efficiency of SPSG in solving this class of problems.