Global Convergence Analysis Of Nonconvex Sparse Regularization Problems

With the rapid development of storage technology and computer computing capabilities,we can collect,store,transmit,and process many data easily.The ability has been rapidly improved,and many algorithm models like deep neural networks have emerged.These models are often non-convex,and there is often strong redundancy between data or parameters.This paper considers a class of sparse,regularity and non-convex optimization problem,we design the algorithm and give the analysis of the global convergence,finally we design the experiment to verify the validity of the algorithm.The structure of the paper as follows:In the chapter 1,we talk about corresponding background,related basic concepts and preliminary knowledge of the thesis.In the chapter 2,we discuss the application of nonconvex optimization problems and the related problems of sparse regularization.In the chapter 3,we propose the proximal gradient descent algorithm to solve the model,and prove its global convergence.In the chapter 4,the simulation experiment on the data set verifies the effectiveness of the algorithm.