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On interval branch-and-bound for additively separable functions with common variables

Author

Listed:
  • J. Berenguel
  • L. Casado
  • I. García
  • E. Hendrix
  • F. Messine

Abstract

Interval branch-and-bound (B&B) algorithms are powerful methods which look for guaranteed solutions of global optimisation problems. The computational effort needed to reach this aim, increases exponentially with the problem dimension in the worst case. For separable functions this effort is less, as lower dimensional sub-problems can be solved individually. The question is how to design specific methods for cases where the objective function can be considered separable, but common variables occur in the sub-problems. This paper is devoted to establish the bases of B&B algorithms for separable problems. New B&B rules are presented based on derived properties to compute bounds. A numerical illustration is elaborated with a test-bed of problems mostly generated by combining traditional box constrained global optimisation problems, to show the potential of using the derived theoretical basis. Copyright The Author(s) 2013

Suggested Citation

  • J. Berenguel & L. Casado & I. García & E. Hendrix & F. Messine, 2013. "On interval branch-and-bound for additively separable functions with common variables," Journal of Global Optimization, Springer, vol. 56(3), pages 1101-1121, July.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:3:p:1101-1121
    DOI: 10.1007/s10898-012-9928-x
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    Citations

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    Cited by:

    1. Jon Lee & Daphne Skipper & Emily Speakman & Luze Xu, 2023. "Gaining or Losing Perspective for Piecewise-Linear Under-Estimators of Convex Univariate Functions," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 1-35, January.
    2. Jens Deussen & Uwe Naumann, 2023. "Subdomain separability in global optimization," Journal of Global Optimization, Springer, vol. 86(3), pages 573-588, July.
    3. Jan Kronqvist & Andreas Lundell & Tapio Westerlund, 2018. "Reformulations for utilizing separability when solving convex MINLP problems," Journal of Global Optimization, Springer, vol. 71(3), pages 571-592, July.

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