Properties and iterative methods for the lasso and its variants (Q741471)

The author introduces several new iterative algorithms based on the proximal map and proves the convergence of the generated sequences. The results are applied to approximate a solution of the minizimization problem \[ \min_{x}{1 \over 2} \|Ax-b\|_{2}^{2} {\;subject\;to\;}\|x\|_{1}\leq t, \] known as least absolute shrinkage operator (or lasso) and first introduced in [\textit{R. Tibshirani}, J. R. Stat. Soc., Ser. B 58, No. 1, 267--288 (1996; Zbl 0850.62538)]. Convergence theorems for solving two variants of lasso are also proved.