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Proving Strong Duality for Geometric Optimization Using a Conic Formulation

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  • François Glineur

Abstract

Geometric optimization 1 is an important class of problems that has many applications, especially in engineering design. In this article, we provide new simplified proofs for the well-known associated duality theory, using conic optimization. After introducing suitable convex cones and studying their properties, we model geometric optimization problems with a conic formulation, which allows us to apply the powerful duality theory of conic optimization and derive the duality results valid for geometric optimization. Copyright Kluwer Academic Publishers 2001

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:105:y:2001:i:1:p:155-184:10.1023/a:1013357600036
    DOI: 10.1023/A:1013357600036
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    Cited by:

    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. 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.
    3. Qinghong Zhang & Kenneth O. Kortanek, 2019. "On a Compound Duality Classification for Geometric Programming," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 711-728, March.
    4. 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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