Journal of Global Optimization

, Volume 60, Issue 2, pp 145–164 | Cite as

Upper bounding in inner regions for global optimization under inequality constraints

  • Ignacio Araya
  • Gilles TrombettoniEmail author
  • Bertrand Neveu
  • Gilles Chabert


In deterministic continuous constrained global optimization, upper bounding the objective function generally resorts to local minimization at several nodes/iterations of the branch and bound. We propose in this paper an alternative approach when the constraints are inequalities and the feasible space has a non-null volume. First, we extract an inner region, i.e., an entirely feasible convex polyhedron or box in which all points satisfy the constraints. Second, we select a point inside the extracted inner region and update the upper bound with its cost. We describe in this paper two original inner region extraction algorithms implemented in our interval B&B called IbexOpt (AAAI, pp 99–104, 2011). They apply to nonconvex constraints involving mathematical operators like , \( +\; \bullet ,\; /,\; power,\; sqrt,\; exp,\; log,\; sin\). This upper bounding shows very good performance obtained on medium-sized systems proposed in the COCONUT suite.


Global optimization Upper bounding Intervals  Branch and bound  Inner regions Interval Taylor 


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Ignacio Araya
    • 1
  • Gilles Trombettoni
    • 2
    Email author
  • Bertrand Neveu
    • 3
  • Gilles Chabert
    • 4
  1. 1.UTFSMUniversitad Federico Santa MariaValparaisoChile
  2. 2.IRIT, LIRMMUniversité Montpellier 2MontpellierFrance
  3. 3.Imagine LIGM Université Paris–EstChamps-sur-MarneFrance
  4. 4.LINAEcole de Mines de NantesNantesFrance

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