A Continuous Method Of Sparse Optimization Problems

In recent years,Dave data sparse representation and sparse reconstruction algorithm is one of research hot spots in the field of optimization,and is widely used in computer science and technology,image recognition,radar positioning,medical detection and artificial intelligence,and many other fields.In the case that the data itself is sparse,the data output by a set of complete base linear expressions is used to reconstruct the original data under certain sparse conditions.The problem of sparse optimization mainly comes from the problem of compressed sensing.Compressed sensing is a new theoretical framework,mainly through a small amount of measurement data to recover the original signal process.We use data sparse,improve the ability of collecting data and the ability to process information,to reduce the large amounts of data in the process of sampling,storage,transmission and analysis of redundant burden,and in these process,sparse optimization has played a pivotal role,is also our key to solve the problem.We obtain the optimal solution by solving the sparse optimization model.Sparse optimization is a very forward branch in the field of optimization.There are many algorithms for solving the sparse optimization model,such as alternating direction method(ADMM),delineated approximation algorithm and so on.In this paper,the homotopy algorithm(continuous algorithm)is used to solve the problem of sparse optimization.The main content of the study is the smoothness of the model,the equivalence of the model,the structure of homotopy equation,the existence of homotopy path and the global convergence of the algorithm.Continuity method of prominent advantages is that it has a wide range of convergence or overall convergence of the homotopy method to the requirement of the selection of initial approximation solution is relatively broad,don't need to solve the full close.This article first introduces several commonly used methods for solving sparse optimization problem,and then for a class of sparse optimization problem,adopted the method of coagulation function involves smoothing sparse optimization model,and presents a smooth after the model and the equivalence of the original problem,obtained after smooth convex programming is the problem.In this paper,we construct homotopy mapping,prove the existence and boundlessness of homotopy path,establish a kind of continuous algorithm of sparse optimization problem,and prove the convergence of the algorithm.Numerical examplesshow that the algorithm is effective and feasible.