Proving strong duality for geometric optimization using a conic formulation

Proving strong duality for geometric optimization using a conic formulation

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Article ID: iaor20023006
Country: Netherlands
Volume: 105
Issue: 1
Start Page Number: 155
End Page Number: 184
Publication Date: Jul 2001
Journal: Annals of Operations Research
Authors:
Keywords: duality
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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