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Proving Strong Duality for Geometric Optimization Using a Conic Formulation

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Abstract

Geometric optimization1 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.

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  1. Service de Mathématique et de Recherche Opérationnelle, Faculté Polytechnique de Mons, Rue de Houdain, 9, B-7000, Mons, Belgium

    François Glineur

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  1. François Glineur
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Glineur, F. Proving Strong Duality for Geometric Optimization Using a Conic Formulation. Annals of Operations Research 105, 155–184 (2001). https://doi.org/10.1023/A:1013357600036

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