Summary
In this work, approximate solutions of vector optimization problems in the sense of Tanaka [18] are characterized via scalarization. Necessary and sufficient conditions are obtained using a new order representing property and a new monotonicity concept, respectively. A family of gauge functions defined by generalized Chebyshev norms and verifying both properties is introduced in order to characterize approximate solutions of vector optimization problems via approximate solutions of several scalarizations.
This research was partially supported by the Ministerio de Ciencia y Tecnología (Spain), project BFM2003-02194.
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Gutiérrez, C., Jiménez, B., Novo, V. (2007). Optimality Conditions for Tanaka’s Approximate Solutions in Vector Optimization. In: Generalized Convexity and Related Topics. Lecture Notes in Economics and Mathematical Systems, vol 583. Springer, Berlin, Heidelberg . https://doi.org/10.1007/978-3-540-37007-9_16
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DOI: https://doi.org/10.1007/978-3-540-37007-9_16
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