A UNIFIED CONIC FORMULATION FOR CONVEX PROBLEMS INVOLVING POWERS
François Glineur, joint work with Robert Chares

This talk introduces a common framework unifying several classes of 
convex optimization problems including linear programming, second-order 
cone programming, quadratically constrained convex quadratic programming, 
$l_p$ programming, minimization of sums of Euclidean or $p$-norms, geometric 
programming and entropy programming. Any of these problems can be modelled 
as a conic optimization problem, where every cone used in the formulation 
is the conic hull of the epigraph of some convex power function 
$x \mapsto |x|^p$ for $p \ge 1$. 

Moreover, every such cone is self-dual, which implies that the dual for 
every instance belonging to this problem class also belongs to the same class.

We will also explain how problems involving exponential and logarithmic 
functions can actually obtained as limit cases when $p \to \infty$.

A solver for this problem class will be described in another talk 
("Solving convex problems involving powers with a conic interior-point algorithm").