caa a22 4500 475769759 CHVBK 20180406123616.0 cr unu---uuuuu 170329e20000801xx s 000 0 eng 10.1007/s101070050019 doi (NATIONALLICENCE)springer-10.1007/s101070050019 Kummer Bernd Humboldt-University Berlin, Math.-Nat. Fak. II, Institute of Mathematics, 10099 Berlin, Germany, e-mail: kummer@mathematik.hu-berlin.de, DE aut Inverse functions of pseudo regular mappings and regularity conditions [Elektronische Daten] [Bernd Kummer] 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. Springer-Verlag Berlin Heidelberg, 2000 metric regularity nationallicence intersection of multifunctions nationallicence inverse functions nationallicence descent directions nationallicence nonsmooth equations nationallicence Ekeland points nationallicence generalized derivatives nationallicence stationary points Mathematics Subject Classification (1991) nationallicence 90C31, 90C48, 70H30 nationallicence Mathematical Programming Springer-Verlag 88/2(2000-08-01), 313-339 0025-5610 88:2<313 2000 88 10107 https://doi.org/10.1007/s101070050019 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s101070050019 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kummer Bernd Humboldt-University Berlin, Math.-Nat. Fak. II, Institute of Mathematics, 10099 Berlin, Germany, e-mail: kummer@mathematik.hu-berlin.de, DE aut NATIONALLICENCE 773 0- Mathematical Programming Springer-Verlag 88/2(2000-08-01), 313-339 0025-5610 88:2<313 2000 88 10107 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer