PLW Algorithm Based On Elastic-Net Regularization Model

Projected Landweber iteration algorithm is a matrix restoration algorithm,which combines projection tool and Landweber iteration.Landweber iteration can minimize the objective function in the model,meanwhile the matrix projection operator can make the algorithm iteration running within the constraints.PLW algorithm is an adaptive fixed point continuation algorithm,which recovers the matrix faster under the same conditions.At present,PLW algorithm has studied nuclear norm regularization model,however,some researches show that the result is unstable when we use the nuclear norm regularization model to recover the matrix with strong correlation.Therefore,this paper constructs PLW algorithm of the elastic-net regularization model and discusses the error bounds of the algorithm and the stability and effectiveness of the algorithm.Specifically,the main work of this paper includes the following aspects:(1)We construct FPC algorithm of the elastic-net regularization model.At first,we give the equation about the solution of optimization model according to the properties of subdifferential and the expression of matrix nuclear norm,and then we get the solution which is expressed by the vector thresholding operator according to the condition of satisfying the equation.So that we attain the FPC algorithm of the elastic-net regularization model.Finally,we deduce the convergence of FPC algorithm according to the nonexpansion of the vector thresholding operator,.(2)This paper focuses on the PLW algorithm of the elastic-net regularization model.At first,the optimization model is transformed from the nuclear norm regularization model to the elastic-net regularization model.Because Landweber iteration minimize the objective function in the optimization model,and the projection operator make the algorithm iteration running within the nonlinear constraints.So,we attain the PLW algorithm of the elastic-net regularization model.Then we get the relationship between the projection operator and the vector thresholding operator according to the properties of the vector thresholding operator,Further we get the relationship between the PLW algorithm and FPC algorithm of the elastic-net regularization model.Finally we deduce the error bound of algorithm under the condition of the matrix restricted isometry property.(3)PLW algorithm of the elastic-net regularization model and nuclear norm regularization model are used to recover the data matrix with strong correlation,and the experimental results shows that the elastic-net regularization model is more stable.