Iterative re-weighted least squares algorithm for l-minimization with tight frame and 0 < p ≤ 1

Mathematical model of infection kinetics and its analysis for COVID-19, SARS and MERS

“…We selected these four cycles of MERS cases for analysis. The software 1stOpt and its Levenberg-Marquardt optimization algorithm (Bi and Liang, 2018;Liang and Clay, 2019) were used to fit Eq. (3).…”

Improved iteratively reweighted least squares algorithms for sparse recovery problem

“…Lemma (This is a special case that $$D$$ equals to the unit matrix I in [13]. ) Assume that $$A$$ has the $$\beta$$‐$$\mathrm{NSP}$$ of order $$K$$ with constant $$\gamma &lt;1$$.…”

“…So it is desirable to develop efficient algorithms for $$0&lt;\tau &lt;1$$. Many algorithms have been proposed to solve (), such as Alternating Direction Method (ADM) [8], Iterative Shrinkage‐Thresholding (IST) [9], Gradient Projection (GP) [10], Iteratively Reweight $$\ell _1$$ (IRL1) [3, 11, 12] and Iteratively Reweighted Least Squares (IRLS) [13–15]. Liang and Clay [13] studied the IRLS algorithm to solve the $$\ell _p$$ minimization with a tight frame, and proved the asymptotic regularity and convergence of the sequence $$\lbrace x^n\rbrace$$ that is generated by this algorithm.…”

“…Liang and Clay [13] studied the IRLS algorithm to solve the $$\ell _p$$ minimization with a tight frame, and proved the asymptotic regularity and convergence of the sequence $$\lbrace x^n\rbrace$$ that is generated by this algorithm. It is worth pointing out that when the tight frame is the identity matrix, the method in [13] is equivalent to the method in [16]. Miosso et al.…”

“…Many algorithms have been proposed to solve (3), such as Alternating Direction Method (ADM) [8], Iterative Shrinkage-Thresholding (IST) [9], Gradient Projection (GP) [10], Iteratively Reweight 𝓁 1 (IRL1) [3,11,12] and Iteratively Reweighted Least Squares (IRLS) [13][14][15]. Liang and Clay [13] studied the IRLS algorithm to solve the 𝓁 p minimization with a tight frame, and proved the asymptotic regularity and convergence of the sequence {x n } that is generated by this algorithm. It is worth pointing out that when the tight frame is the identity matrix, the method in [13] is equivalent to the method in [16].…”