caa a22 4500 46316900X CHVBK 20180406164808.0 cr unu---uuuuu 170326e20070501xx s 000 0 eng 10.1007/s10957-007-9173-5 doi (NATIONALLICENCE)springer-10.1007/s10957-007-9173-5 Sach P. Institute of Mathematics, Hanoi, Vietnam aut Moreau-Rockafellar Theorems for Nonconvex Set-Valued Maps [Elektronische Daten] [P. Sach] In this paper, we introduce the notion of (Benson) proper subgradient of a set-valued map and prove that, for some class of nonconvex set-valued maps, a proper subgradient of the sum of two set-valued maps can be expressed as the sum of two proper subgradients of these maps. This property is also established for weak subgradients. A result in Ref.[Lin, L.J.: J. Math. Anal. Appl. 186, 30-51 (1994)], obtained under some convexity assumption, is included as a special case of the corresponding result of this paper. Springer Science+Business Media, LLC, 2007 Moreau-Rockafellar theorem nationallicence Benson proper subgradients nationallicence Set-valued maps nationallicence Generalized convexity nationallicence Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 133/2(2007-05-01), 213-227 0022-3239 133:2<213 2007 133 10957 https://doi.org/10.1007/s10957-007-9173-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10957-007-9173-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Sach P. Institute of Mathematics, Hanoi, Vietnam aut NATIONALLICENCE 773 0- Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 133/2(2007-05-01), 213-227 0022-3239 133:2<213 2007 133 10957 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer