Lagrangian Duality in Set-Valued Optimization
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- 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.