Upper bounding in inner regions for global optimization under inequality constraints

Ignacio Araya (), Gilles Trombettoni (), Bertrand Neveu () and Gilles Chabert ()

Journal of Global Optimization, 2014, vol. 60, issue 2, 145-164

Abstract: 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 , $$ +\; \bullet ,\; /,\; power,\; sqrt,\; exp,\; log,\; sin$$ + ∙ , / , p o w e r , s q r t , e x p , l o g , s i n . This upper bounding shows very good performance obtained on medium-sized systems proposed in the COCONUT suite. Copyright Springer Science+Business Media New York 2014

Keywords: Global optimization; Upper bounding; Intervals; Branch and bound; Inner regions; Interval Taylor (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s10898-014-0145-7

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