加权平方 $\ell_{2,\infty}$ 范数的邻近算子及其应用
Proximity operator of the weighted squared $\ell_{2,\infty}$ norm with applications
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中文总结 AI 辅助
本文为加权平方 $\ell_{2,\infty}$ 范数及其弱凸版本推导出邻近算子的闭式解，并应用于去噪和加权最大最小分散问题。
中文摘要 AI 辅助
本文推导了加权平方 $\ell_{2,\infty}$ 范数的邻近算子的闭式解。此外，我们还推导了该函数的弱凸版本的邻近算子的闭式解。证明过程利用了已知的用于计算上确界函数的邻近算子的结果，这需要求解一个辅助问题。我们通过找到与一阶最优性条件相关的 KKT 乘子和临界点，得到了该辅助问题的显式解。此外，我们还将该方法应用于去噪问题和加权最大最小分散问题。
英文摘要
In this paper, we derive a closed-form for the proximity operator of the weighted squared $\ell_{2,\infty}$ norm. Moreover, we derive a closed-form for the proximity operator of a weakly convex version of this function. The proof involves using known results for compute the proximity operator of a supremum function, which requires finding a solution of an auxiliary problem. We find the explicit solution of this auxiliary problem by finding the KKT multipliers and the critical point associated to the first-order optimality conditions. Additionally, we present applications to denoising problems and weighted max-min dispersion problems.
发表机构
- Universidad Tecnica Federico Santa Maria（智利弗雷德里科·圣塔玛丽亚理工大学）
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