Abstract
We present an interval global optimization algorithm using a modified monotonicity test. The improvement applies to constrained problems and can result in significant speedup, when constraints are sparse, i.e. they “bind” a few of the variables, not all of them. A theorem that ensures the correctness of the new tool, is given and proved. The improved method is applied to an economic problem of setting optimal prices on a couple of products.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Hansen, E.: Global Optimization Using Interval Analysis. Marcel Dekker, New York (1992)
Horst, R., Pardalos, P.M. (eds.): Handbook of Global Optimization. Kluwer, Dordrecht (1995)
Kearfott, R.B.: A Review of Techniques in the Verified Solution of Constrained Global Optimization Problems. In: Kearfott, R.B., Kreinovich, V. (eds.) Applications of Interval Computations, Kluwer, Dordrecht (1996)
Kearfott, R.B.: Rigorous Global Search: Continuous Problems. Kluwer, Dordrecht (1996)
Kearfott, R.B., Nakao, M.T., Neumaier, A., Rump, S.M., Shary, S.P., van Hentenryck, P.: Standardized notation in interval analysis, available at http://www.mat.univie.ac.at/~neum/software/int/notation.ps.gz
Kubica, B.J., Malinowski, K.: An Interval Global Optimization Algorithm Combining Symbolic Rewriting and Componentwise Newton Method Applied to Control a Class of Queueing Systems. Reliable Computing 11(5), 393–411 (2005)
Malinowski, K.: PriceStrat 4.0 Initial Research Paper. KSS Internal Document, Manchester (2000)
Michalewicz, Z., Fogel, D.B.: How to Solve It: Modern Heuristics. Springer, Heidelberg (2004)
Neumaier, A.: Complete Search in Continuous Global Optimization and Constraint Satisfaction. In: Acta Numerica, pp. 271–369. Cambridge University Press, Cambridge (2004)
Simon, H.: Price Management. North-Holland (1989)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kubica, B.J., Niewiadomska-Szynkiewicz, E. (2007). An Improved Interval Global Optimization Method and Its Application to Price Management Problem. In: Kågström, B., Elmroth, E., Dongarra, J., Waśniewski, J. (eds) Applied Parallel Computing. State of the Art in Scientific Computing. PARA 2006. Lecture Notes in Computer Science, vol 4699. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75755-9_123
Download citation
DOI: https://doi.org/10.1007/978-3-540-75755-9_123
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75754-2
Online ISBN: 978-3-540-75755-9
eBook Packages: Computer ScienceComputer Science (R0)