- Constructing self-concordant barriers for convex cones Yurii Nesterov (nesterovcore.ucl.ac.be) Abstract: In this paper we develop a technique for constructing self-concordant barriers for convex cones. We start from a simple proof for a variant of standard result on transformation of a $\nu$-self-concordant barrier for a set into a self-concordant barrier for its conic hull with parameter $(3.08 \sqrt{\nu} + 3.57)^2$. Further, we develop a convenient composition theorem for constructing barriers directly for convex cones. In particular, we can construct now good barriers for several interesting cones obtained as a conic hull of epigraph of a univariate function. This technique works for power functions, entropy, logarithm and exponent function, etc. It provides a background for development of polynomial-time methods for separable optimization problems. Thus, our abilities in constructing good barriers for convex sets and cones become now identical. Keywords: interior-point methods, self-concordant barriers, conic problem, barrier calculus Category 1: Linear, Cone and Semidefinite Programming (Other ) Citation: CORE Discussion Paper 2006/30, March 2006 Download: [PDF]Entry Submitted: 04/03/2006Entry Accepted: 04/03/2006Entry Last Modified: 04/03/2006Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.