Conic optimization: An elegant framework for convex optimization

Conic optimization: An elegant framework for convex optimization

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Article ID: iaor20032502
Country: Belgium
Volume: 41
Issue: 1/2
Start Page Number: 5
End Page Number: 28
Publication Date: Jan 2001
Journal: Belgian Journal of Operations Research, Statistics and Computer Science
Authors:
Keywords: duality, l-norm
Abstract:

The purpose of this survey article is to introduce the reader to a very elegant formulation of convex optimization problems called conic optimization and outline its many advantages. After a brief introduction to convex optimization, the notion of convex cone is introduced, which leads to the conic formulation of convex optimization problems. This formulation features a very symmetric dual problem, and several useful duality theorems pertaining to this conic primal–dual pair are presented. The usefulness of this approach is then demonstrated with its application to a well-known class of convex problems called lp-norm optimization. A suitably defined convex cone leads to a conic formulation for this problem, which allows us to derive its dual and associated weak and strong duality properties in a seamless manner.

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