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Primal-dual interior-point methods with asymmetric barrier

Yurii Nesterov(Yurii.Nesterov***at***uclouvain.be)

Abstract: In this paper we develop several polynomial-time interior-point methods (IPM) for solving nonlinear primal-dual conic optimization problem. We assume that the barriers for the primal and the dual cone are not conjugate. This broken symmetry does not allow to apply the standard primal-dual IPM. However, we show that in this situation it is also possible to develop very efficient optimization methods, which satisfy all desired qualities, including the infeasible-start features. Our technique is based on asymmetric primal-dual barrier augmented by squared residual of the primal-dual linear system.

Keywords: conic optimization, self-concordant barriers, primal-dual interior-point methods

Category 1: Applications -- Science and Engineering

Citation: CORE Discussion Paper 2008/57

Download: [PDF]

Entry Submitted: 09/17/2008
Entry Accepted: 09/17/2008
Entry Last Modified: 09/17/2008

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