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Optimized choice of parameters in interior-point methods for linear programming

Abstract

In this work, we propose a predictor–corrector interior point method for linear programming in a primal–dual context, where the next iterate is chosen by the minimization of a polynomial merit function of three variables: the first is the steplength, the second defines the central path and the third models the weight of a corrector direction. The merit function minimization is performed by restricting it to constraints defined by a neighborhood of the central path that allows wide steps. In this framework, we combine different directions, such as the predictor, the corrector and the centering directions, with the aim of producing a better one. The proposed method generalizes most of predictor–corrector interior point methods, depending on the choice of the variables described above. Convergence analysis of the method is carried out, considering an initial point that has a good practical performance, which results in Q-linear convergence of the iterates with polynomial complexity. Numerical experiments using the Netlib test set are made, which show that this approach is competitive when compared to well established solvers, such as PCx.

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Acknowledgements

We thank the anonymous referees for their valuable suggestions that improved the presentation of this work.

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Correspondence to Luiz-Rafael Santos.

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This research was sponsored by Brazilian Agencies Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) (Grants 08/09685-8 and 10/06822-4) and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq).

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Santos, LR., Villas-Bôas, F., Oliveira, A.R.L. et al. Optimized choice of parameters in interior-point methods for linear programming. Comput Optim Appl 73, 535–574 (2019). https://doi.org/10.1007/s10589-019-00079-9

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Keywords

  • Linear programming
  • Infeasible interior point methods
  • Optimized choice of parameters

Mathematics Subject Classification

  • 49M15
  • 65K05
  • 90C05
  • 90C51