Proving strong duality for geometric optimization using a conic formulation

Glineur, François
(2001) Annals of Operations Research — Vol. 105, n° 1/4, p. 155-184 (2001)

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Abstract
Geometric optimization 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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Glineur, F. (2001). Proving strong duality for geometric optimization using a conic formulation. Annals of Operations Research, 105(1/4), 155-184. https://doi.org/10.1023/A:1013357600036 (Original work published 2001)