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Optimality Conditions for Tanaka’s Approximate Solutions in Vector Optimization

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Generalized Convexity and Related Topics

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 583))

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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Authors and Affiliations

  1. Departamento de Matemática Aplicada, E.T.S.I. Informática, Universidad de Valladolid, Edificio de Tecnologías de la Información y las Telecomunicaciones, Campus Miguel Delibes, s/n, 47011, Valladolid, Spain

    César Gutiérrez

  2. Departamento de Matemática Aplicada, E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia, c/ Juan del Rosal, 12, Ciudad Universitaria, 28040, Madrid, Spain

    Bienvenido Jiménez & Vicente Novo

Authors
  1. César Gutiérrez
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  2. Bienvenido Jiménez
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  3. Vicente Novo
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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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