Optimization Method Based On Double Sparse Problem

Sparse optimization is an important research issue in optimization methods.It has applications in fields such as compression sensing,signal processing,machine learning,and computer image processing.Compression sensing is a research hot point in sparse optimization problems,and has been favored by scholars and ex-perts due to its advantages of low storage costs and hardware complexity.The compression sensing model studied in this paper contains dual sparse constraints.Due to the non-convex and discontinuous nature of the problem,the Moreau en-velope function is first used to approximate the objective function,approximating the model to a non-convex continuous function.Then,a forward-reflect-backward splitting（FRB）algorithm and a FRB function are proposed for this problem.Un-der appropriate conditions,the finite length property of the iterative sequence of the algorithm is proved using the FRB function.Finally,assuming that the FRB function has the Kurdyka-Lojasiewicz（KL）property with exponent₂¹,the global convergence and convergence rate of the algorithm are proved.