The Iterative Reweighted L₁ Minimization Algorithm For Sparse Vector Linear Optimization Problem

Sparse optimization problem is a non-convex,discontinuous and NP-hard combinatorial optimization problem,which is usually solved by direct or indirect methods.Since the direct method has a large amount of calculation and is easy to find the local optimal solution,many scholars both at home and abroad have used indirect method to solve the sparse optimization problem.The so-called indirect method is to relax the sparse optimization problem into continu-ous optimization problem,which include convex relaxation problem and non-convex relaxation problem.When the number of rows of the matrix A is less than the number of columns,the matrix is said to be undetermined,and the corresponding original problem is called to solve the sparse solution of an undetermined linear system.This paper mainly studies the sparse so-lution of the undetermined linear system.Since CWB algorithm transforms the sparse vector optimization problem into a constrained optimization problem,the sparse vector optimization problem in our paper is transformed into an unconstrained optimization problem by the penal-ized function.In addition the weight of CWB algorithm is improved to obtain a new iterative reweighted L1 minimization algorithm,and we give the convergence analysis of the algorithm.Numerical experiments show,when we use the algorithm to recover sparse data,the recovery effect of our algorithm is not worse than CWB algorithm,and is better than L1 algorithm.This paper is divided into four chapters:The first chapter introduces the research back-ground,research status and the main content and frame structure of the whole paper.In the second chapter,we give the original and approximate model of sparse recovery of underdeter-mined linear system,and some preliminary knowledge which is prepared for the subsequent proof of the algorithm.In the third chapter,we introduce parameters to get the approximate model,solve it by new iterative reweighted L1 minimization algorithm,and give the conver-gence,convergence rate and error bounds of the algorithm.In the fourth chapter,we present a numerical experiment for sparse data recovery with new iterative reweighted L1 minimization algorithm,and compare it with CWB algorithm and L1 algorithm.