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Lipschitzian inverse functions, directional derivatives, and applications inC 1,1 optimization

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Abstract

The paper shows that Thibault's limit sets allow an iff-characterization of local Lipschitzian invertibility in finite dimension. We consider these sets as directional derivatives and extend the calculus in a way that can be used to clarify whether critical points are strongly stable inC 1,1 optimization problems.

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Authors and Affiliations

  1. Department of Mathematics, Humboldt University Berlin, Berlin, Germany

    B. Kummer (Associate Professor)

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  1. B. Kummer
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Communicated by A. V. Fiacco

Many fruitful discussions with colleagues D. Klatte and K. Tammer as well as with H. Th. Jongen and F. Nozicka have influenced the present investigations in a very constructive manner. For the original papers concerning the sets Δf(x; u), the author is indebted to Prof. L. Thibault.

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Kummer, B. Lipschitzian inverse functions, directional derivatives, and applications inC 1,1 optimization. J Optim Theory Appl 70, 561–582 (1991). https://doi.org/10.1007/BF00941302

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