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Interior-Point Lagrangian Decomposition Method for Separable Convex Optimization

Author

Listed:
  • I. Necoara

    (University Politehnica Bucharest
    Katholieke Universiteit Leuven)

  • J. A. K. Suykens

    (Katholieke Universiteit Leuven)

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.

Suggested Citation

  • I. Necoara & J. A. K. Suykens, 2009. "Interior-Point Lagrangian Decomposition Method for Separable Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 143(3), pages 567-588, December.
    • Handle: RePEc:spr:joptap:v:143:y:2009:i:3:d:10.1007_s10957-009-9566-8
    DOI: 10.1007/s10957-009-9566-8
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    References listed on IDEAS

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    1. M. Hegland & M.R. Osborne & J. Sun, 2001. "Parallel Interior Point Schemes for Solving Multistage Convex Programming," Annals of Operations Research, Springer, vol. 108(1), pages 75-85, November.
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    Cited by:

    1. Jueyou Li & Guo Chen & Zhaoyang Dong & Zhiyou Wu, 2016. "A fast dual proximal-gradient method for separable convex optimization with linear coupled constraints," Computational Optimization and Applications, Springer, vol. 64(3), pages 671-697, July.
    2. Deyi Liu & Quoc Tran-Dinh, 2020. "An Inexact Interior-Point Lagrangian Decomposition Algorithm with Inexact Oracles," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 903-926, June.
    3. Quoc Tran Dinh & Ion Necoara & Moritz Diehl, 2014. "Path-following gradient-based decomposition algorithms for separable convex optimization," Journal of Global Optimization, Springer, vol. 59(1), pages 59-80, May.
    4. Da Tian, 2015. "An exterior point polynomial-time algorithm for convex quadratic programming," Computational Optimization and Applications, Springer, vol. 61(1), pages 51-78, May.
    5. Bingfeng Bai & Wei Fan, 2023. "Research on strategic liner ship fleet planning with regard to hub-and-spoke network," Operations Management Research, Springer, vol. 16(1), pages 363-376, March.

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