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Monotonic Optimization: Branch and Cut Methods

In: Essays and Surveys in Global Optimization

Author

Listed:
  • Hoang Tuy
  • Faiz Al-Khayyal
  • Phan Thien Thach

Abstract

Monotonic optimization is concerned with optimization problems dealing with multivariate monotonic functions and differences of monotonic functions. For the study of this class of problems a general framework (Tuy, 2000a) has been earlier developed where a key role was given to a separation property of solution sets of monotonic inequalities similar to the separation property of convex sets. In the present paper the separation cut is combined with other kinds of cuts, called reduction cuts, to further exploit the monotonic structure. Branch and cuts algorithms based on an exhaustive rectangular partition and a systematic use of cuts have proved to be much more efficient than the original polyblock and copolyblock outer approximation algorithms.

Suggested Citation

  • Hoang Tuy & Faiz Al-Khayyal & Phan Thien Thach, 2005. "Monotonic Optimization: Branch and Cut Methods," Springer Books, in: Charles Audet & Pierre Hansen & Gilles Savard (ed.), Essays and Surveys in Global Optimization, chapter 0, pages 39-78, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-25570-5_2
    DOI: 10.1007/0-387-25570-2_2
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    Cited by:

    1. Hoang Tuy, 2010. "$${{\mathcal {D}(\mathcal {C})}}$$ -optimization and robust global optimization," Journal of Global Optimization, Springer, vol. 47(3), pages 485-501, July.

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