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Characterizing Efficiency on Infinite-dimensional Commodity Spaces with Ordering Cones Having Possibly Empty Interior

Author

Listed:
  • Fabián Flores-Bazán

    (Universidad de Concepción)

  • Fernando Flores-Bazán

    (Universidad del Bío Bío)

  • Sigifredo Laengle

    (Universidad de Chile)

Abstract

Some production models in finance require infinite-dimensional commodity spaces, where efficiency is defined in terms of an ordering cone having possibly empty interior. Since weak efficiency is more tractable than efficiency from a mathematical point of view, this paper characterizes the equality between efficiency and weak efficiency in infinite-dimensional spaces without further assumptions, like closedness or free disposability. This is obtained as an application of our main result that characterizes the solutions to a unified vector optimization problem in terms of its scalarization. Standard models as efficiency, weak efficiency (defined in terms of quasi-relative interior), weak strict efficiency, strict efficiency, or strong solutions are carefully described. In addition, we exhibit two particular instances and compute the efficient and weak efficient solution set in Lebesgue spaces.

Suggested Citation

  • Fabián Flores-Bazán & Fernando Flores-Bazán & Sigifredo Laengle, 2015. "Characterizing Efficiency on Infinite-dimensional Commodity Spaces with Ordering Cones Having Possibly Empty Interior," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 455-478, February.
    • Handle: RePEc:spr:joptap:v:164:y:2015:i:2:d:10.1007_s10957-014-0558-y
    DOI: 10.1007/s10957-014-0558-y
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    References listed on IDEAS

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    1. Jean-Marc Bonnisseau & Bertrand Crettez, 2007. "On the Characterization of Efficient Production Vectors," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(2), pages 213-223, May.
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    7. Fabián Flores-Bazán & Sigifredo Laengle & Gino Loyola, 2013. "Characterizing the efficient points without closedness or free-disposability," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(2), pages 401-410, March.
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    Cited by:

    1. Khushboo & C. S. Lalitha, 2018. "Scalarizations for a unified vector optimization problem based on order representing and order preserving properties," Journal of Global Optimization, Springer, vol. 70(4), pages 903-916, April.
    2. Shiva Kapoor & C. S. Lalitha, 2019. "Stability in unified semi-infinite vector optimization," Journal of Global Optimization, Springer, vol. 74(2), pages 383-399, June.
    3. Khushboo & C. S. Lalitha, 2019. "A unified minimal solution in set optimization," Journal of Global Optimization, Springer, vol. 74(1), pages 195-211, May.
    4. Shiva Kapoor & C. S. Lalitha, 2019. "Stability and Scalarization for a Unified Vector Optimization Problem," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 1050-1067, September.
    5. Shiva Kapoor & C. S. Lalitha, 2021. "Essential stability in unified vector optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 161-175, May.
    6. Nguyen Dinh & Miguel A. Goberna & Dang H. Long & Marco A. López-Cerdá, 2019. "New Farkas-Type Results for Vector-Valued Functions: A Non-abstract Approach," Journal of Optimization Theory and Applications, Springer, vol. 182(1), pages 4-29, July.

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