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Explicit Characterization of the $\ell_p$ Proximity Operator for $0<p<1$
Researchers provide an explicit characterization of the scalar proximal map for the nonconvex $\ell_p$ quasi-norm with $0<p<1$, detailing its threshold structure and solution conditions. The study applies the Lagrange–Bürmann inversion to analyze the stationarity equation for robust evaluation.
This work addresses the challenge of evaluating the proximity operator for a powerful sparsity surrogate, which is important for optimization problems in signal processing and machine learning. Understanding these operators can improve algorithm robustness and solution accuracy.
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Score 74
Source Type arxiv
Reposts 0
Topic Quality 51
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