Lagrangian Duality in Set-Valued Optimization

E. Hernández () and L. Rodríguez-Marín ()
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E. Hernández: Universidad Nacional de Educación a Distancia
L. Rodríguez-Marín: Universidad Nacional de Educación a Distancia

Journal of Optimization Theory and Applications, 2007, vol. 134, issue 1, No 9, 119-134

Abstract: Abstract 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.

Keywords: Set-valued maps; Set optimization; Lagrangian duality; Saddle points (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10957-007-9237-6

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