A New Inclusion Function for Optimization: Kite&mdashlThe One Dimensional Case
Journal of Global Optimization
Tight convex underestimators for $${{\mathcal C}^2}$$-continuous problems: I. univariate functions
Journal of Global Optimization
Interval oriented multi-section techniques for global optimization
Journal of Computational and Applied Mathematics
A review of recent advances in global optimization
Journal of Global Optimization
On lower bounds using additively separable terms in interval b&b
ICCSA'12 Proceedings of the 12th international conference on Computational Science and Its Applications - Volume Part III
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The performance of interval analysis branch-and-bound global optimization algorithms strongly depends on the efficiency of selection, bounding, elimination, division, and termination rules used in their implementation. All the information obtained during the search process has to be taken into account in order to increase algorithm efficiency, mainly when this information can be obtained and elaborated without additional cost (in comparison with traditional approaches). In this paper a new way to calculate interval analysis support functions for multiextremal univariate functions is presented. The new support functions are based on obtaining the same kind of information used in interval analysis global optimization algorithms. The new support functions enable us to develop more powerful bounding, selection, and rejection criteria and, as a consequence, to significantly accelerate the search. Numerical comparisons made on a wide set of multiextremal test functions have shown that on average the new algorithm works almost two times faster than a traditional interval analysis global optimization method.