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On generalized trade-off directions in nonconvex multiobjective optimization

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Abstract.

Trade-off information related to Pareto optimal solutions is important in multiobjective optimization problems with conflicting objectives. Recently, the concept of trade-off directions has been introduced for convex problems. These trade-offs are characterized with the help of tangent cones. Generalized trade-off directions for nonconvex problems can be defined by replacing convex tangent cones with nonconvex contingent cones. Here we study how the convex concepts and results can be generalized into a nonconvex case. Giving up convexity naturally means that we need local instead of global analysis.

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Authors and Affiliations

  1. Department of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35 (Agora), FIN-40351 Jyväskylä, Finland, e-mail: {miettine,makela}@mit.jyu.fi, , , , , , FI

    Kaisa Miettinen & Marko M. Mäkelä

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  1. Kaisa Miettinen
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  2. Marko M. Mäkelä
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Received: December 2000 / Accepted: October 2001¶Published online February 14, 2002

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Miettinen, K., Mäkelä, M. On generalized trade-off directions in nonconvex multiobjective optimization. Math. Program. 92, 141–151 (2002). https://doi.org/10.1007/s101070100282

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  • DOI: https://doi.org/10.1007/s101070100282

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