Inverse functions of pseudo regular mappings and regularity conditions |
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Authors: | Bernd Kummer |
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Institution: | (1) Humboldt-University Berlin, Math.-Nat. Fak. II, Institute of Mathematics, 10099 Berlin, Germany, e-mail: kummer@mathematik.hu-berlin.de, DE |
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Abstract: | We show that, even for monotone directionally differentiable Lipschitz functionals on Hilbert spaces, basic concepts of generalized
derivatives identify only particular pseudo regular (or metrically regular) situations. Thus, pseudo regularity of (multi-)
functions will be investigated by other means, namely in terms of the possible inverse functions. In this way, we show how
pseudo regularity for the intersection of multifunctions can be directly characterized and estimated under general settings
and how contingent and coderivatives may be modified to obtain sharper regularity conditions. Consequences for a concept of
stationary points as limits of Ekeland points in nonsmooth optimization will be studied, too.
Received: May 20, 1999 / Accepted: February 15, 2000?Published online July 20, 2000 |
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Keywords: | : metric regularity – intersection of multifunctions – inverse functions – descent directions – nonsmooth equations – Ekeland points – generalized derivatives – stationary points Mathematics Subject Classification (1991): 90C31 90C48 70H30 |
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