%0 Journal Article
%T An Efficient Adaptive Iteratively Reweighted <font style="font-family:Mistral; font-size:20pt;"><i>l</i></font><sub>1</sub> Algorithm for Elastic <font style="font-family:Mistral; font-size:20pt;"><i>l</i></font><sub>q</sub> Regularization
%A Yong Zhang
%A Wanzhou Ye
%J Advances in Pure Mathematics
%P 498-506
%@ 2160-0384
%D 2016
%I Scientific Research Publishing
%R 10.4236/apm.2016.67036
%X In this paper, we propose an efficient adaptive iteratively reweighted <span style=\"font-family:Mistral;font-size:20pt;\"><i>l</i></span><sub>1</sub> algorithm (A-IRL1 algorithm) for solving the elastic <span style=\"font-family:Mistral;font-size:20pt;\"><i>l</i></span><sub>q</sub> regularization problem. We prove that the sequence generated by the A-IRL1 algorithm is convergent for any rational <img src=\"Edit_c8c18ebd-ae28-4505-8459-b1cc4468aeff.png\" alt=\"\" /> and the limit is a critical point of the elastic <span style=\"font-family:Mistral;font-size:20pt;\"><i>l</i></span><sub>q</sub> regularization problem. Under certain conditions, we present an error bound for the limit point of convergent sequence.
%K Compressed Sensing
%K Elastic &lt
%K font style=&quot
%K font-family:Mistral
%K font-size:20pt
%K &quot
%K &gt
%K &lt
%K i&gt
%K l&lt
%K /i&gt
%K &lt
%K /font&gt
%K &lt
%K sub&gt
%K q&lt
%K /sub&gt
%K Minimization
%K Nonconvex Optimization
%K Convergence
%K Critical Point
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=67409