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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
Department of Mathematics, College of Science, Shanghai University, Shanghai, China
Department of Mathematics, College of Science, Shanghai University, Shanghai, China
- 1 Department of Mathematics, College of Science, Shanghai University, Shanghai, China
- 2 Department of Mathematics, College of Science, Shanghai University, Shanghai, China
Advances in Pure Mathematics·Volume 06 (2016)·Pages 498–506·Published 14 June 2016·DOI10.4236/apm.2016.67036
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Abstract
In this paper, we propose an efficient adaptive iteratively reweighted l 1 algorithm (A-IRL1 algorithm) for solving the elastic l q regularization problem. We prove that the sequence generated by the A-IRL1 algorithm is convergent for any rational and the limit is a critical point of the elastic l q regularization problem. Under certain conditions, we present an error bound for the limit point of convergent sequence.
KeywordsCompressed SensingElastic <font style="font-family:Mistralfont-size:20pt"><i>l</i></font><sub>q</sub>MinimizationNonconvex OptimizationConvergenceCritical Point
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