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An Extension of the Kaliszewski Cone to Non-polyhedral Pointed Cones in Infinite-Dimensional Spaces

Author

Listed:
  • Lidia Huerga

    (E.T.S.I. Industriales Universidad Nacional de Educación a Distancia)

  • Baasansuren Jadamba

    (Rochester Institute of Technology)

  • Miguel Sama

    (E.T.S.I. Industriales Universidad Nacional de Educación a Distancia)

Abstract

In this paper, we propose an extension of the family of constructible dilating cones given by Kaliszewski (Quantitative Pareto analysis by cone separation technique, Kluwer Academic Publishers, Boston, 1994) from polyhedral pointed cones in finite-dimensional spaces to a general family of closed, convex, and pointed cones in infinite-dimensional spaces, which in particular covers all separable Banach spaces. We provide an explicit construction of the new family of dilating cones, focusing on sequence spaces and spaces of integrable functions equipped with their natural ordering cones. Finally, using the new dilating cones, we develop a conical regularization scheme for linearly constrained least-squares optimization problems. We present a numerical example to illustrate the efficacy of the proposed framework.

Suggested Citation

  • Lidia Huerga & Baasansuren Jadamba & Miguel Sama, 2019. "An Extension of the Kaliszewski Cone to Non-polyhedral Pointed Cones in Infinite-Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 437-455, May.
    • Handle: RePEc:spr:joptap:v:181:y:2019:i:2:d:10.1007_s10957-018-01468-6
    DOI: 10.1007/s10957-018-01468-6
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    References listed on IDEAS

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    1. B. Jadamba & A. Khan & M. Sama, 2017. "Error estimates for integral constraint regularization of state-constrained elliptic control problems," Computational Optimization and Applications, Springer, vol. 67(1), pages 39-71, May.
    2. Ghate, Archis, 2015. "Circumventing the Slater conundrum in countably infinite linear programs," European Journal of Operational Research, Elsevier, vol. 246(3), pages 708-720.
    3. Mas-Colell, Andreu & Zame, William R., 1991. "Equilibrium theory in infinite dimensional spaces," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 34, pages 1835-1898, Elsevier.
    4. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, September.
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