Primal-dual interior-point methods with asymmetric barriers

Yurii Nesterov
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Yurii Nesterov: Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE)

No 2008057, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

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; polynomial-time methods; interior-point methods; path-following methods; potential-reduction methods; infeasible start. (search for similar items in EconPapers)
Date: 2008-10-01
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