锥形平均映射的模及其在两个子空间夹角中的应用
Modulus of conically averaged mappings and its applications to angles between two subspaces
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中文总结 AI 辅助
研究提出锥形平均模对映射分类，引入相关值并研究其联系，在线性情形刻画矩阵并给出公式，计算子空间夹角，建立非线性结果，还研究了次凸函数相关映射的锥形平均性。
中文摘要 AI 辅助
锥形平均映射是平均映射的推广，在众多优化算法中很重要。本文提出锥形平均模来对其分类，引入广义单调映射的单调和共单调值并研究它们与锥形平均模的联系。在线性情形下，完全刻画了锥形平均矩阵并给出计算平均模的显式公式。作为应用，计算了两个子空间间的迪克米尔角和弗里德里克斯角，还建立了非线性结果及研究了次凸函数的近端和反射映射的锥形平均性。
英文摘要
Conically averaged mappings, a generalization of averaged mappings, are important in a wide range of Optimization Algorithms. In this paper, we propose the modulus of conical averagedness to classify conical averaged mappings. Introducing the monotone and comonotone values of generalized monotone mappings, we investigate their connections to the modulus of conical averagedness. In the linear setting, we completely characterize conically averaged matrices, and derive explicit and pleasing formulae for computing their modulus of averagedness. As applications, we compute the Dixmier and Friedrichs angles between two subspaces. Nonlinear results are established as extensions of the linear case. Conical averagedness of proximal and reflection mappings of hypoconvex functions are also studied.
