Integration of multivalued operators and cyclic submonotonicity |
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| Authors: | Aris Daniilidis Pando Georgiev Jean-Paul Penot |
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| Affiliation: | Laboratoire de Mathématiques Appliquées, CNRS ERS 2055, Université de Pau et des Pays de l'Adour, avenue de l'Université, 64000 Pau, France ; Sofia University ``St. Kl. Ohridski', Faculty of Mathematics and Informatics, 5 J. Bourchier Blvd., 1126 Sofia, Bulgaria ; Laboratoire de Mathématiques Appliquées, CNRS ERS 2055, Université de Pau et des Pays de l'Adour, avenue de l'Université, 64000 Pau, France |
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| Abstract: | We introduce a notion of cyclic submonotonicity for multivalued operators from a Banach space  to its dual. We show that if the Clarke subdifferential of a locally Lipschitz function is strictly submonotone on an open subset  of  , then it is also maximal cyclically submonotone on  , and, conversely, that every maximal cyclically submonotone operator on  is the Clarke subdifferential of a locally Lipschitz function, which is unique up to a constant if  is connected. In finite dimensions these functions are exactly the lower C functions considered by Spingarn and Rockafellar. |
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| Keywords: | Integration subdifferential submonotone operator subsmooth function |
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