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Towards nonsymmetric conic optimization

Yurii Nesterov (nesterov***at***core.ucl.ac.be)

Abstract: In this paper we propose a new interior-point method, which is based on an extension of the ideas of self-scaled optimization to the general cones. We suggest using the primal correction process to find a {\em scaling point}. This point is used to compute a strictly feasible primal-dual pair by simple projection. Then, we define an affine-scaling direction and perform a prediction step. This is the only moment when the dual barrier is used. Thus, we need only to compute its value, which can even be done approximately. In the second part of the paper we develop a $4n$-self-concordant barrier for $n$-dimensional $p$-cone, which can be used for numerical testing of the proposed technique.

Keywords: Conic optimization, interior-point methods, self-concordant barriers, affine-scaling direction, p-norm cones

Category 1: Linear, Cone and Semidefinite Programming (Other )

Citation: CORE Discussion Paper 2006/28, March 2006

Download: [PDF]

Entry Submitted: 03/31/2006
Entry Accepted: 03/31/2006
Entry Last Modified: 03/31/2006

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