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Existence and Boundedness of Solutions in Infinite-Dimensional Vector Optimization Problems

Author

Listed:
  • César Gutiérrez

    (Universidad de Valladolid)

  • Rubén López

    (Universidad Católica de la Ssma. Concepción)

  • Vicente Novo

    (Universidad Nacional de Educación a Distancia)

Abstract

This work focuses on the nonemptiness and boundedness of the sets of efficient and weak efficient solutions of a vector optimization problem, where the decision space is a normed space and the image space is a locally convex Hausdorff topological linear space. By studying certain boundedness and coercivity concepts of vector-valued functions and via an asymptotic analysis, we extend to this kind of problems some well-known existence and boundedness results for efficient and weak efficient solutions of multiobjective optimization problems with Pareto or polyhedral orderings. Some of these results are proved under weaker assumptions.

Suggested Citation

  • César Gutiérrez & Rubén López & Vicente Novo, 2014. "Existence and Boundedness of Solutions in Infinite-Dimensional Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 515-547, August.
    • Handle: RePEc:spr:joptap:v:162:y:2014:i:2:d:10.1007_s10957-014-0541-7
    DOI: 10.1007/s10957-014-0541-7
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    References listed on IDEAS

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    Cited by:

    1. F. Fakhar & H. R. Hajisharifi & Z. Soltani, 2023. "Noncoercive and noncontinuous equilibrium problems: existence theorem in infinite-dimensional spaces," Journal of Global Optimization, Springer, vol. 86(4), pages 989-1003, August.
    2. Yarui Duan & Liguo Jiao & Pengcheng Wu & Yuying Zhou, 2022. "Existence of Pareto Solutions for Vector Polynomial Optimization Problems with Constraints," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 148-171, October.
    3. César Gutiérrez & Rubén López, 2020. "On the Existence of Weak Efficient Solutions of Nonconvex Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 880-902, June.
    4. César Gutiérrez & Lidia Huerga & Vicente Novo & Lionel Thibault, 2015. "Chain Rules for a Proper $$\varepsilon $$ ε -Subdifferential of Vector Mappings," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 502-526, November.

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