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Characterizing generalized trade-off directions

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Abstract.

Recently, so-called trade-off directions have been introduced for convex multiobjective optimization problems and, later, they have been generalized for nonconvex problems. The trade-off directions are characterized with the help of tangent and contingent cones. Trade-offs give information about the interrelations of the changes in the objective function values in different Pareto optimal solutions. Such information is valuable when searching for the most preferable Pareto optimal solution. Here, we introduce characterizations of generalized trade-off directions using the tools of nonsmooth analysis. In this way, it is possible to analytically describe concepts that originally were geometrical.

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Manuscript received: June 2002/Final version received: September 2002

Acknowledgement. This research was supported by the grants 65760 and 8583 of the Academy of Finland.

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Miettinen, K., Mäkelä, M. Characterizing generalized trade-off directions. Mathematical Methods of OR 57, 89–100 (2003). https://doi.org/10.1007/s001860200247

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  • DOI: https://doi.org/10.1007/s001860200247

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