Abstract
In order to show necessary conditions for approximate solutions of vector-valued optimization problems in general spaces, we introduce an axiomatic approach for a scalarization scheme. Several examples illustrate this scalarization scheme. Using an Ekeland-type variational principle by Isac [12] and suitable scalarization techniques, we prove the optimality conditions under different assumptions concerning the ordering cone and under certain differentiability assumptions for the objective function.
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Dedicated to the memory of Professor George Isac
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Isac, G., Tammer, C. (2010). Application of a Vector-Valued Ekeland-Type Variational Principle for Deriving Optimality Conditions. In: Pardalos, P., Rassias, T., Khan, A. (eds) Nonlinear Analysis and Variational Problems. Springer Optimization and Its Applications, vol 35. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0158-3_23
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DOI: https://doi.org/10.1007/978-1-4419-0158-3_23
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