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Dynamic updates of the barrier parameter in primal-dual methods for nonlinear programming

P Armand (paul.armand***at***unilim.fr)
J Benoist (joel.benoist***at***unilim.fr)
D Orban (dominique.orban***at***polymtl.ca)

Abstract: We introduce a framework in which updating rules for the barrier parameter in primal-dual interior-point methods become dynamic. The original primal-dual system is augmented to incorporate explicitly an updating function. A Newton step for the augmented system gives a primal-dual Newton step and also a step in the barrier parameter. Based on local information and a linesearch, the decrease of the barrier parameter is automatically adjusted. We analyze local convergence properties, report numerical experiments on a standard collection of nonlinear problems and compare our results to a state-of-the-art interior-point implementation. In many instances, the adaptive algorithm reduces the number of iterations and of function evaluations. Its design guarantees a better fit between the magnitudes of the primal-dual residual and of the barrier parameter along the iterations.

Keywords: constrained optimization, interior point method, nonlinear programming, primal-dual method, barrier method

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Rapport de recherche 2005-05 Laboratoire LACO, Universite de Limoges, France September 2005.

Download: [Postscript][PDF]

Entry Submitted: 10/03/2005
Entry Accepted: 10/03/2005
Entry Last Modified: 06/06/2006

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