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Consider the minimization problem described this paper. Let $f_{\lambda}$ be the minimizer. As a part of extending my work, I am able to show the following facts $$\lim_\limits{\lambda \to 0}\|f_{\lambda}\| = 0$$ and $$\lim_\limits{\lambda \to \infty}\|f_{\lambda}\| = 0$$ My problem now is (as ...