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Christian Günther(Christian.Guenthermathematik.unihalle.de) Abstract: In this paper, the aim is to compute Pareto efficient solutions of multiobjective optimization problems involving forbidden regions. More precisely, we assume that the vectorvalued objective function is componentwise generalizedconvex and acts between a real topological linear preimage space and a finite dimensional image space, while the feasible set is given by the whole preimage space without some forbidden regions that are defined by convex sets. This leads us to a nonconvex multiobjective optimization problem. Using the recently proposed penalization approach by Günther and Tammer (2017), we show that the solution set of the original problem can be generated by solving a finite family of unconstrained multiobjective optimization problems. We apply our results to a special multiobjective location problem (known as pointobjective location problem) where the aim is to locate a new facility in a continuous location space (a finitedimensional Hilbert space) in the presence of a finite number of demand points. For the choice of the new location point, we are taking into consideration some forbidden regions that are given by open balls (defined w.r.t. the underlying norm). For such a nonconvex location problem, under the assumption that the forbidden regions are pairwise disjoint, we give complete geometrical descriptions for the sets of (strictly, weakly) Pareto efficient solutions by using the approach by Günther and Tammer (2017) and results derived by Jourani, Michelot and Ndiaye (2009). Keywords: Multiobjective optimization; Pareto efficiency; Generalizedconvexity; Location theory; Forbidden regions; Euclidean norm Category 1: Other Topics (MultiCriteria Optimization ) Category 2: Convex and Nonsmooth Optimization (Generalized Convexity/Monoticity ) Category 3: Applications  Science and Engineering (Facility Planning and Design ) Citation: Preprint (October 31, 2017), Martin Luther University HalleWittenberg, Faculty of Natural Sciences II, Institute for Mathematics, 06099 Halle (Saale), Germany (submitted) Download: [PDF] Entry Submitted: 10/31/2017 Modify/Update this entry  
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