Generalized leibniz rules and lipschitzian stability for expected-integral mappings

Abstract

This paper is devoted to the study of the expected-integral multifunctions given in the form E-Phi (x) := integral(T) Phi(t)(x)d mu, where Phi: T x R-n paired right arrows R-m is a set-valued mapping on a measure space (T, A, mu). Such multifunctions appear in applications to stochastic programming, which require developing efficient calculus rules of generalized differentiation. Major calculus rules are developed in this paper for coderivatives of multifunctions E-Phi and second-order subdifferentials of the corresponding expected-integral functionals with applications to constraint systems arising in stochastic programming. The paper is self-contained with presentation in the preliminaries of some needed results on sequential first-order subdifferential calculus of expected-integral functionals taken from the first paper of this series.