Regular Castaing Representations of Multifunctions with Applications to Stochastic Programming SIAM Journal on Optimization Volume 10, Number 3 pp. Our aim is to construct a Castaing representation which inherits the regularity properties of the multifunction. The construction uses Steiner points. A notion of a generalized Steiner point is introduced. A Castaing representation called regular is defined by using generalized Steiner selections.
All selections are measurable, continuous, resp.
H lder-continuous, or directionally differentiable, if the multifunction has the corresponding properties. The results are applied to various multifunctions arising in stochastic programming. In particular, statements about the asymptotic behavior of measurable selections of solution sets via the delta-method are obtained. Steiner center, selections, Castaing representation, stochastic programs, random sets, delta-theorems AMS Subject Classifications . 54C65, 28B20, 90C15 PII .