具有非线性缩放的透视函数的邻近算子
Proximity Operators of Perspective Functions with Nonlinear Scaling
AI总结：
针对非线性缩放透视函数非光滑、一阶算法需计算邻近算子的问题，本文用基函数与缩放函数的邻近算子给出了 Hilbert 空间中该邻近算子的闭式表达式。
摘要：
透视函数是一种构造，它将定义在给定空间上的基函数与定义在另一空间上的非线性缩放函数结合起来，并在乘积空间上产生一个下半连续凸函数。由于透视函数通常是非光滑的，将其用于一阶算法需要计算其邻近算子。本文建立了定义在 Hilbert 空间上的透视函数邻近算子的闭式表达式，该表达式通过涉及其基函数的邻近算子和涉及其缩放函数的邻近算子来表示。
英文摘要：
A perspective function is a construction which combines a base function defined on a given space with a nonlinear scaling function defined on another space and which yields a lower semicontinuous convex function on the product space. Since perspective functions are typically nonsmooth, their use in first-order algorithms necessitates the computation of their proximity operator. This paper establishes closed-form expressions for the proximity operator of a perspective function defined on a Hilbert space in terms of a proximity operator involving its base function and one involving its scaling function.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
