Journal of Optimization Theory and Applications

, Volume 134, Issue 1, pp 119–134

Lagrangian Duality in Set-Valued Optimization


DOI: 10.1007/s10957-007-9237-6

Cite this article as:
Hernández, E. & Rodríguez-Marín, L. J Optim Theory Appl (2007) 134: 119. doi:10.1007/s10957-007-9237-6


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. A necessary condition and a sufficient condition for the existence of saddle points are given.


Set-valued mapsSet optimizationLagrangian dualitySaddle points

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Departamento de Matemática AplicadaUniversidad Nacional de Educación a DistanciaMadridSpain