Quasidifferentiabilities of the expectation functions of random quasidifferentiable functions
Sida Lin, Ming Z. Huang, Zun-Quan Xia, Dan Li · Optimization · 2020
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.