Nonmonotonic Gradient Projection Algorithm For Sparse Optimization With Spherical Constraints

Sparse constrained optimization problems have been widely used in digital signal processing,image processing,compression sensing,machine learning and other fields.Efficient and feasible algorithms for solving sparse optimization problems have momentous theoretical significance and application value,attracting a lot of attention from scholars at home and abroad.In this paper,a nonmonotone gradient projection algorithm is proposed to solve the sparse optimization problem with spherical constraints in the following form(?)Where f:Rn→ Ris a continuously differentiable function,Ds={x∈Rn:‖x‖0≤s},DB={x∈Rn:‖x‖22≤1}.Under appropriate assumptions,we study the global convergence of the nonmono-tone gradient projection algorithm.It is proved that the convergence point of the iterative sequence generated by the nonmonotone gradient projection algorithm is the L-stable point of the spherical constrained sparse optimization problem,and we also use the augmented Lagrangian multiplier method to solve the shadow problem.The numerical results show that the nonmonotone gradient projection algorithm can solve sparse optimization problems with spherical constraints quickly and effectively.The paper is divided into five chapters,the main structure is as follows:In the first chapter,the application background and research status of sparse constrained optimization problem are introduced.Moreover,some symbols in this paper are demonstrated and explained.Finally,we give the mathematical model of spherical constrained sparse optimization problem,explaining the main contents of this paper.The second chapter,some basic assumptions,definitions and Lemma are in-troduced,and the nonmonotone gradient projection algorithm for solving convex constrained optimization problems is briefly reviewed.The third chapter,a solution to the sparse optimization problem with spherical constraints(1.1)is given and the global convergence of the nonmonotone gradient projection algorithm is studied.The forth chapter,the subproblem of nonmonotone gradient projection algo-rithm is solved by using lagrangian multiplier method(3.1).The fifth chapter,The feasibility and high efficiency of nonmonotonic gradient projection algorithm are verified by numerical experiments.