Another Face of DIRECT

L Chiter (chiterlyahoo.fr)

Abstract: It is shown that, contrary to a claim of [D. E. Finkel, and C. T. Kelley, Additive scaling and the DIRECT algorithm, J. Glob. Optim. 36 (2006) 597-608], it is possible to divide the smallest hypercube which contains the low function value by considering hyperrectangles whose points are located on the diagonal of the center point of this hypercube using a division procedure which influences the slope to be below the threshold fmin - epsilon |fmin| and thus reduces the influence of the parameter epsilon.

Keywords: DIRECT, Global Optimization, Geometrical Interpretation.

Category 1: Global Optimization

Category 2: Global Optimization (Theory )

Category 3: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Mathematics Department, Setif University, 19000 Algeria

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Entry Submitted: 07/24/2007
Entry Accepted: 07/27/2007
Entry Last Modified: 07/31/2007

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