Minchenko, L. I. Multivalued analysis and differential properties of multivalued mappings. (English. Russian original) Zbl 1056.49021 J. Math. Sci., New York 116, No. 3, 3266-3302 (2003). 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. Reviewer: Valerii V. Obukhovskij (Voronezh) Cited in 1 ReviewCited in 5 Documents 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 Keywords:multivalued map; marginal function; derivative; directional derivative; subdifferential PDFBibTeX XMLCite \textit{L. I. Minchenko}, J. Math. Sci., New York 116, No. 3, 3266--3302 (2003; Zbl 1056.49021) Full Text: DOI