Conic optimization: an elegant framework for convex optimization
(2001) Belgian Journal of Operations Research, Statistics and Computer Science — Vol. 41, n° 1-2, p. 5-28 (2001)
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- 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 $l_p$-norm optimization. A suitably defined convex cone leads to a conic formulation for this problem, which allows us to derive its dual and the associated weak and strong duality properties in a seamless manner.
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Citations
Glineur, F. (2001). Conic optimization: an elegant framework for convex optimization. Belgian Journal of Operations Research, Statistics and Computer Science, 41(1-2), 5-28. https://hdl.handle.net/2078.5/269333 (Original work published 2001)