{
  "id": "2101.06711",
  "version": "v1",
  "published": "2021-01-17T16:52:14.000Z",
  "updated": "2021-01-17T16:52:14.000Z",
  "title": "Generalized Differentiation of Expected-Integral Mappings with Applications to Stochastic Programming, II: Leibniz Rules and Lipschitz Stability",
  "authors": [
    "Boris S. Mordukhovich",
    "Pedro Pérez-Aros"
  ],
  "comment": "26 pages",
  "categories": [
    "math.OC"
  ],
  "abstract": "This paper is devoted to the study of the expected-integral multifunctions given in the form \\begin{equation*} \\operatorname{E}_\\Phi(x):=\\int_T\\Phi_t(x)d\\mu, \\end{equation*} where $\\Phi\\colon T\\times\\mathbb{R}^n \\rightrightarrows \\mathbb{R}^m$ is a set-valued mapping on a measure space $(T,\\mathcal{A},\\mu)$. 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 $\\operatorname{E}_\\Phi$ 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 presenting in the preliminaries some needed results on sequential first-order subdifferential calculus of expected-integral functionals taken from the first paper of this series.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-17T16:52:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49J53",
      "90C15",
      "90C34",
      "49J52"
    ],
    "keywords": [
      "stochastic programming",
      "generalized differentiation",
      "expected-integral mappings",
      "leibniz rules",
      "lipschitz stability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}