Multivalued analysis and differential properties of multivalued mappings (Q1417350)

Let \(X\) and \(Y\) be finite-dimensional spaces; \(F: X \rightarrow 2^Y\) a multimap and \(f: X \times Y \rightarrow \mathbb{R}\) a function. The functions \(\varphi, \Phi : X \rightarrow \mathbb{R} \cup \{\pm \infty\},\) \[ \varphi (x) = \inf \{f(x,y) | y \in F(x)\}, \] \[ \Phi (x) = \sup \{f(x,y) | y \in F(x)\} \] are said to be marginal functions of \(F\). The paper is the survey of differential properties of multimaps and corresponding marginal functions and their interconnections. No proofs are given. The bibliography contains 177 items.