Attempts to approximate a set-valued mapping

Demyanov, V.F., Lemarechal, C., & Zowe, J. (1985). Attempts to approximate a set-valued mapping. In: Nondifferentiable Optimization: Motivations and Applications. Eds. Demyanov, V.F. & Pallaschke, D., pp. 3-7 Berlin/Heidelberg, Germany: Springer. ISBN 978-3-662-12603-5 10.1007/978-3-662-12603-5_1.

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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.

Item Type: Book Section
Research Programs: System and Decision Sciences - Core (SDS)
Depositing User: Romeo Molina
Date Deposited: 05 Apr 2016 08:09
Last Modified: 27 Aug 2021 17:40

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