Properties And Iterative Methods For The Elastic Net With L_p-Norm Errors

The paper can be mainly divided into three parts.In the first part(the first two chapters),This paper can be divided into three parts:the first part is the first two chapters,the first chapter is the introduction part,the second chapter is the pre-liminary part,the definition of dual mapping,subdifferential and proximal mapping is given,and the proximal gradient is introduced.Algorithm(fixed point algorith-m),Frank-Wolfe algorithm and some propositions and lemmas,and corresponding explanations and proofs.The three and four chapters of this article focus on the elastic network(p-EN)with the lp-norm error.In Chapter 3,this article introduces some of the basic properties of p-EN,such as the sufficient and necessary condition for the optimal solution bounded by p-EN,the sufficient condition that the optimal solution is 0,and detailed proofs are given.In the fourth chapter,since the gradient of our objective function is not Lipschitz continuous,the proximal gradient algo-rithm can not prove that the sequence generated by the algorithm can converge to the solution of our objective function,so the generalized Frank-Wolfe algorithm is introduced.And prove that the sequence generated by the algorithm can converge to the solution of our objective function.