A Nonmontone Projection Gradient Algorithm For Sparsity Constrained Optimization Problems

Sparsity constrained optimization problems have wide applications in many fields including signal and image processing,machine learning,economics,statistics and so on.It is of theoretical significance and application value to study numer-ical algorithms for solving sparsity constrained optimization problems,which has attracted lots of attention from scholars.In this paper,we propose a novel nonmonotone projection gradient method for solving a class of sparsity constrained optimization problems in the form of where f:R~n?R is continuously differentiable,r is a positive integer,orThis algorithm is based on the nonmonotone line search strategy proposed by Zhang and Hager[SIAM J.Optim.,2004,14(4):1043-1056].Under suitable conditions,we analyze the convergence of the algorithm.In particular,we prove that each accumu-lation point of the sequence of iterates generated by the algorithm is a L-stationary point of the sparsity constrained optimization problems.Numerical results show the efficiency and the feasibility of the proposed algorithm.