Abstract
As is well known the proximal iterative method can be used to solve the lasso of Tibshirani (J. R. Stat. Soc., Ser. B 58:267-288, 1996). In this paper, we first propose a modified proximal iterative method based on the viscosity approximation method to obtain strong convergence, then we apply this method to solve the lasso.
Highlights
The lasso of Tibshirani [ ] is formulated as the minimization problem min x∈RnAx – b subject to x ≤ t, ( . )where A is an m × n matrix, b ∈ Rm, t ≥ is a tuning parameter
As the norm promotes the sparsity phenomenon that occurs in practical problems such as image/signal processing, machine learning and so on, the lasso has received much attention in recent years
It is proved that the algorithm we propose can obtain strong convergence
Summary
The lasso of Tibshirani [ ] is formulated as the minimization problem min x∈RnAx – b subject to x ≤ t, ( . )where A is an m × n (real) matrix, b ∈ Rm, t ≥ is a tuning parameter. Xu [ ] exploited the following proximal algorithm: xn+ = proxλng ◦ (I – λn∇f ) xn to solve lasso Their iterative algorithms only obtain weak convergence. ) can converge strongly to a fixed point x∗ of T, which is the unique solution of the variational inequality (I – f )x∗, x – x∗ ≥ , for x ∈ Fix(T).
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