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As a natural extension of the nonnegative elastic net penalty method, ARGEN is proved to have both variable selection consistency and estimation consistency under some conditions. The asymptotic behavior in distribution of the ARGEN estimators have been studied in this framework. We also propose an algorithm called MU-QP-RR-W-<jats:inline-formula><jats:alternatives><jats:tex-math>$$l_1$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>l<\/mml:mi><mml:mn>1<\/mml:mn><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula>to efficiently solve the ARGEN problem. By conducting simulation study we show that ARGEN outperforms the elastic net in a number of settings. 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