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Conic Formulation for l p -Norm Optimization

Author

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  • F. Glineur

    (Service de Mathématique et de Recherche Opérationnelle, Faculté Polytechnique de Mons)

  • T. Terlaky

    (McMaster University)

Abstract

In this paper, we formulate the l p -norm optimization problem as a conic optimization problem, derive its duality properties (weak duality, zero duality gap, and primal attainment) using standard conic duality and show how it can be solved in polynomial time applying the framework of interior-point algorithms based on self-concordant barriers.

Suggested Citation

  • F. Glineur & T. Terlaky, 2004. "Conic Formulation for l p -Norm Optimization," Journal of Optimization Theory and Applications, Springer, vol. 122(2), pages 285-307, August.
    • Handle: RePEc:spr:joptap:v:122:y:2004:i:2:d:10.1023_b:jota.0000042522.65261.51
    DOI: 10.1023/B:JOTA.0000042522.65261.51
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    References listed on IDEAS

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    1. F. Glineur & T. Terlaky, 2004. "Conic Formulation for l p -Norm Optimization," Journal of Optimization Theory and Applications, Springer, vol. 122(2), pages 285-307, August.
    2. François Glineur, 2001. "Proving Strong Duality for Geometric Optimization Using a Conic Formulation," Annals of Operations Research, Springer, vol. 105(1), pages 155-184, July.
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    Cited by:

    1. F. Glineur & T. Terlaky, 2004. "Conic Formulation for l p -Norm Optimization," Journal of Optimization Theory and Applications, Springer, vol. 122(2), pages 285-307, August.
    2. Robert Chares & François Glineur, 2008. "An interior-point method for the single-facility location problem with mixed norms using a conic formulation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(3), pages 383-405, December.
    3. Yue Lu & Ching-Yu Yang & Jein-Shan Chen & Hou-Duo Qi, 2020. "The decompositions with respect to two core non-symmetric cones," Journal of Global Optimization, Springer, vol. 76(1), pages 155-188, January.
    4. Dávid Papp & Sercan Yıldız, 2022. "Alfonso: Matlab Package for Nonsymmetric Conic Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 11-19, January.
    5. Baha Alzalg, 2016. "The Algebraic Structure of the Arbitrary-Order Cone," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 32-49, April.
    6. Jinchuan Zhou & Yu-Lin Chang & Jein-Shan Chen, 2015. "The H-differentiability and calmness of circular cone functions," Journal of Global Optimization, Springer, vol. 63(4), pages 811-833, December.
    7. Krokhmal, Pavlo A. & Soberanis, Policarpio, 2010. "Risk optimization with p-order conic constraints: A linear programming approach," European Journal of Operational Research, Elsevier, vol. 201(3), pages 653-671, March.

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    1. Robert Chares & François Glineur, 2008. "An interior-point method for the single-facility location problem with mixed norms using a conic formulation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(3), pages 383-405, December.
    2. Yue Lu & Ching-Yu Yang & Jein-Shan Chen & Hou-Duo Qi, 2020. "The decompositions with respect to two core non-symmetric cones," Journal of Global Optimization, Springer, vol. 76(1), pages 155-188, January.
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    7. Dávid Papp & Sercan Yıldız, 2022. "Alfonso: Matlab Package for Nonsymmetric Conic Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 11-19, January.

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