Staff Publications

Staff Publications

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    'Staff publications' is the digital repository of Wageningen University & Research

    'Staff publications' contains references to publications authored by Wageningen University staff from 1976 onward.

    Publications authored by the staff of the Research Institutes are available from 1995 onwards.

    Full text documents are added when available. The database is updated daily and currently holds about 240,000 items, of which 72,000 in open access.

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Record number 436291
Title On lower bounds using separable terms in interval B&B for one-dimensional poblems
Author(s) Berenguel, J.L.; Casado, L.G.; García, I.; Hendrix, E.M.T.; Messine, F.
Source In: Proceedings of the Global Optimization Workshop 2012, 26-29 June 2012, Natal, Brazil / Aloise, D., Hansen, P., Rocha, C., URFN - p. 39 - 42.
Department(s) Operations Research and Logistics
WASS
Publication type Contribution in proceedings
Publication year 2012
Abstract Interval Branch-and-Bound (B&B) algorithms are powerful methods which aim for guaranteed solutions of Global Optimization problems. Lower bounds for a function in a given interval can be obtained directly with Interval Arithmetic. The use of lower bounds based on Taylor forms show a faster convergence to the minimum with decreasing size of the search interval. Our research focuses on one dimensional functions that can be decomposed into several terms (sub-functions). The question is whether using this characteristic leads to sharper bounds when based on bounds of the sub-functions. This paper deals with separable functions in two sub-functions. The use of the separability is investigated for the so-called Baumann form and Lower Bound Value Form (LBVF). It is proven that using the additively separability in the LBVF form may lead to a combination of linear minorants that are sharper than the original one. Numerical experiments confirm this improving behaviour and also show that not all separable methods do always provide sharper additively lower bounds. Additional research is needed to obtain better lower bounds for multiplicatively separable functions and to address higher dimensional problems.
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