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Recent Progress in Interior-Point Methods: Cutting-Plane Algorithms and Warm Starts

In: Handbook on Semidefinite, Conic and Polynomial Optimization

Author

Listed:
  • Alexander Engau

    (University of Colorado Denver)

Abstract

We review some of the recent enhancements of interior-point methods for the improved solution of semidefinite relaxations in combinatorial optimization and binary quadratic programming. Central topics include general interior-point cutting-plane schemes, handling of linear inequalities, and several warm-starting strategies. A practical implementation and computational results are also discussed.

Suggested Citation

  • Alexander Engau, 2012. "Recent Progress in Interior-Point Methods: Cutting-Plane Algorithms and Warm Starts," International Series in Operations Research & Management Science, in: Miguel F. Anjos & Jean B. Lasserre (ed.), Handbook on Semidefinite, Conic and Polynomial Optimization, chapter 0, pages 471-498, Springer.
    • Handle: RePEc:spr:isochp:978-1-4614-0769-0_17
    DOI: 10.1007/978-1-4614-0769-0_17
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    Cited by:

    1. Gicquel, C. & Lisser, A. & Minoux, M., 2014. "An evaluation of semidefinite programming based approaches for discrete lot-sizing problems," European Journal of Operational Research, Elsevier, vol. 237(2), pages 498-507.
    2. Alexander Engau & Miguel Anjos & Immanuel Bomze, 2013. "Constraint selection in a build-up interior-point cutting-plane method for solving relaxations of the stable-set problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(1), pages 35-59, August.

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