CONIC OPTIMIZATION: AN ELEGANT FRAMEWORK FOR CONVEX OPTIMIZATION

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.