Abstract
The paper briefly presents Topsøe's setup and gives two results based on that. A delta theorem for multifunctions improving that of King [2] is given. In particular, the contingent derivative may be a compact-valued instead of a single-valued multi-function. Stochastic optimization is also discussed. Some results are achieved for the limit distribution of optimal values as well as of optimal solutions.
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References
J.-P. Aubin and H. Frankowska,Set-Valued Analysis (Birkhäuser, Boston, 1990).
A.J. King, Generalized delta theorem for multivalued mappings and measurable selections, Math. Oper. Res. 14 (1989) 720–736.
F. Topsøe, Measurable spaces connected by correspondence, Math. Scand. 30 (1972) 5–45.
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Lachout, P. On multifunction transforms of probability measures. Ann Oper Res 56, 241–249 (1995). https://doi.org/10.1007/BF02031710
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DOI: https://doi.org/10.1007/BF02031710