Abstract

In this paper, we provide an explicit expression for the proximity operator of a perspective of any proper lower semicontinuous convex function defined on a Hilbert space. Our computation enhances and generalizes known formulae for the case when the Fenchel conjugate of the convex function has an open domain or when it is radial. We show numerically that our approach is more efficient than previous approaches in the literature and we provide several examples of nonradial functions for which the domain of its conjugate is not open and we compute the proximity operators of their perspectives.

中文翻译：

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透视函数邻近算子的增强计算

摘要

在本文中，我们为希尔伯特空间上定义的任何真下半连续凸函数的透视的邻近算子提供了显式表达式。我们的计算增强并推广了凸函数的 Fenchel 共轭具有开域或径向时的情况的已知公式。我们在数值上表明，我们的方法比文献中以前的方法更有效，并且我们提供了几个非径向函数的示例，其共轭域不是开放的，并且我们计算了它们的视角的邻近算子。