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Multivalued analysis and differential properties of multivalued mappings. (English. Russian original) Zbl 1056.49021

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.

MSC:

49J53 Set-valued and variational analysis
49J52 Nonsmooth analysis
49K40 Sensitivity, stability, well-posedness
58C06 Set-valued and function-space-valued mappings on manifolds
90C31 Sensitivity, stability, parametric optimization
47H04 Set-valued operators
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