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Quasidifferentiabilities of the expectation functions of random quasidifferentiable functions
Optimization ( IF 1.6 ) Pub Date : 2020-09-09 , DOI: 10.1080/02331934.2020.1818235
Sida Lin 1, 2 , Ming Huang 3 , Zunquan Xia 4 , Dan Li 5
Affiliation  

This paper explores the quasidifferentiabilities (in the sense of Demyanov and Rubinov) of the expectation functions of random quasidifferentiable functions. Under general assumptions, the expectation function of random quasidifferentiable function is quasidifferentiable and the quasidifferentiation and expectation operators can be interchanged. Furthermore, under some conditions, the expectation functions of random K-differentiable function and random K*-differentiable function are K-differentiable and K*-differentiable, respectively, moreover, whose kernelled and adjoint kernelled quasidifferential equal the expectations of kernelled and adjoint kernelled quasidifferential of random K-differentiable function and K*-differentiable function, respectively.



中文翻译:

随机拟可微函数的期望函数的拟可微性

本文探讨了随机拟可微函数的期望函数的拟微分性(在 Demyanov 和 Rubinov 的意义上)。一般假设下,随机拟可微函数的期望函数是拟可微的,且拟微分算子和期望算子可以互换。此外,在某些条件下,随机K-可微函数和随机K*-可微函数的期望函数分别是K-可微和K*-可微,并且其核化和伴随核化拟微分等于核化和伴随核化的期望函数。分别是随机K-可微函数和K*-可微函数的准微分。

更新日期:2020-09-09
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