caa a22 4500 463169026 CHVBK 20180406164808.0 cr unu---uuuuu 170326e20070701xx s 000 0 eng 10.1007/s10957-007-9237-6 doi (NATIONALLICENCE)springer-10.1007/s10957-007-9237-6 Lagrangian Duality in Set-Valued Optimization [Elektronische Daten] [E. Hernández, L. Rodríguez-Marín] In this paper, we study optimization problems where the objective function and the binding constraints are set-valued maps and the solutions are defined by means of set-relations among all the images sets (Kuroiwa, D. in Takahashi, W., Tanaka, T. (eds.) Nonlinear analysis and convex analysis, pp.221-228, 1999). We introduce a new dual problem, establish some duality theorems and obtain a Lagrangian multiplier rule of nonlinear type under convexity assumptions. Anecessary condition and a sufficient condition for the existence of saddle points are given. Springer Science+Business Media, LLC, 2007 Set-valued maps nationallicence Set optimization nationallicence Lagrangian duality nationallicence Saddle points nationallicence Hernández E. Departamento de Matemática Aplicada, Universidad Nacional de Educación a Distancia, Calle Juan del Rosal 12, 28040, Madrid, Spain aut Rodríguez-Marín L. Departamento de Matemática Aplicada, Universidad Nacional de Educación a Distancia, Calle Juan del Rosal 12, 28040, Madrid, Spain aut Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 134/1(2007-07-01), 119-134 0022-3239 134:1<119 2007 134 10957 https://doi.org/10.1007/s10957-007-9237-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10957-007-9237-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hernández E. Departamento de Matemática Aplicada, Universidad Nacional de Educación a Distancia, Calle Juan del Rosal 12, 28040, Madrid, Spain aut NATIONALLICENCE 700 1- Rodríguez-Marín L. Departamento de Matemática Aplicada, Universidad Nacional de Educación a Distancia, Calle Juan del Rosal 12, 28040, Madrid, Spain aut NATIONALLICENCE 773 0- Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 134/1(2007-07-01), 119-134 0022-3239 134:1<119 2007 134 10957 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer