STRONG CONVERGENCE OF AN ITERATIVE METHOD FOR THE LASSO

Abstract

The lasso of Tibshiranis(1996) is a least-squares regularized by the l1 norm. In recent years, the lasso has been paid much attention due to the involvement of the l1 norm, which it’s property is promoted by the sparseness of the norm. Now, we have mostly article studied it’s weak convergence to a solution of the lasso. It is the purpose of this paper to show that under certain conditions, the iterative sequence {x_n} converges strongly to a solution of the lasso, is also the unique solution of the following variational inequality: ⟨(I − h)x^∗,x ̃ − x^∗⟩ ≥ 0, ∀x^∗ ∈ Fix(Vλ), where h : H → H is a contractive mapping and Vλ : H → H is an averaged mapping.