Computational Optimization and Applications

, Volume 41, Issue 1, pp 1–25 | Cite as

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



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 line search, 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.


Constrained optimization Interior point method Nonlinear programming Primal-dual method Barrier method 


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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Université de Limoges, Laboratoire XLIM-UMR CNRS 6172LimogesFrance
  2. 2.Ecole Polytechnique de MontréalMontréalCanada

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