Abstract
In this paper, we provide optimality conditions for approximate proper solutions of a multiobjective optimization problem, whose feasible set is given by a cone constraint and the ordering cone is polyhedral. A first class of optimality conditions is given by means of a nonlinear scalar Lagrangian and the second kind through a linear scalarization technique, under generalized convexity hypotheses, that lets us derive a Kuhn–Tucker multiplier rule.
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Acknowledgements
The authors are very grateful to the anonymous referees for their careful reading and their helpful comments and suggestions. This work was partially supported by Ministerio de Ciencia, Innovación y Universidades (MCIU), Agencia Estatal de Investigación (AEI) (Spain) and Fondo Europeo de Desarrollo Regional (FEDER) under Project PGC2018-096899-B-I00 (MCIU/AEI/FEDER, UE).
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Gutiérrez, C., Huerga, L., Jiménez, B. et al. Optimality conditions for approximate proper solutions in multiobjective optimization with polyhedral cones. TOP 28, 526–544 (2020). https://doi.org/10.1007/s11750-020-00546-1
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DOI: https://doi.org/10.1007/s11750-020-00546-1
Keywords
- Multiobjective optimization
- Optimality conditions
- Approximate proper efficiency
- Polyhedral ordering cone
- Nonlinear Lagrangian
- Linear scalarization