Abstract
Given a multi-valued mapping F, we address the problem of finding another multi-valued mapping H that agrees locally with F in some sense. We show that, contrary to the scalar case, introducing a derivative of F is hardly convenient. For the case when F is convex-compact-valued, we give some possible approximations, and at the same time we show their limitations. The present paper is limited to informal demonstration of concepts and mechanisms. Formal statements and their proofs will be published elsewhere.
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References
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© 1985 Springer-Verlag Berlin Heidelberg
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Demyanov, V.F., Lemaréchal, C., Zowe, J. (1985). Attempts to Approximate a Set-Valued Mapping. In: Demyanov, V.F., Pallaschke, D. (eds) Nondifferentiable Optimization: Motivations and Applications. Lecture Notes in Economics and Mathematical Systems, vol 255. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12603-5_1
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DOI: https://doi.org/10.1007/978-3-662-12603-5_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15979-7
Online ISBN: 978-3-662-12603-5
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