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Interior-Point Lagrangian Decomposition Method for Separable Convex Optimization

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Abstract

In this paper, we propose a distributed algorithm for solving large-scale separable convex problems using Lagrangian dual decomposition and the interior-point framework. By adding self-concordant barrier terms to the ordinary Lagrangian, we prove under mild assumptions that the corresponding family of augmented dual functions is self-concordant. This makes it possible to efficiently use the Newton method for tracing the central path. We show that the new algorithm is globally convergent and highly parallelizable and thus it is suitable for solving large-scale separable convex problems.

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Authors and Affiliations

  1. Automatic Control and Systems Engineering Department, University Politehnica Bucharest, 060042, Bucharest, Romania

    I. Necoara

  2. Department of Electrical Engineering (ESAT), Katholieke Universiteit Leuven, 3001, Leuven–Heverlee, Belgium

    I. Necoara & J. A. K. Suykens

Authors
  1. I. Necoara
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  2. J. A. K. Suykens
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Corresponding author

Correspondence to I. Necoara.

Additional information

Communicated by D.Q. Mayne.

We acknowledge financial support from Flemish Government: FWO Projects G.0226.06, G.0302.07.

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Necoara, I., Suykens, J.A.K. Interior-Point Lagrangian Decomposition Method for Separable Convex Optimization. J Optim Theory Appl 143, 567–588 (2009). https://doi.org/10.1007/s10957-009-9566-8

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  • DOI: https://doi.org/10.1007/s10957-009-9566-8

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