New computer methods for global optimization
New computer methods for global optimization
Cord-slope form of Taylor's expansion in univariate global optimization
Journal of Optimization Theory and Applications
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
Improving Interval Analysis Bounds by Translations
Journal of Global Optimization
A New Inclusion Function for Optimization: Kite&mdashlThe One Dimensional Case
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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Two ways for bounding n-variables functions over a box, based on interval evaluations of first order derivatives, are compared. The optimal Baumann form gives the best lower bound using a center within the box. The admissible simplex form, proposed by the two last authors, uses point evaluations at n + 1 vertices of the box. We show that the Baumann center is within any admissible simplex and can be represented as a linear convex combination of its vertices with coefficients equal to the dual variables of the linear program used to compute the corresponding admissible simplex lower bound. This result is applied in a branch-and-bound global optimization and computational results are reported.