Can interval computations be applied over spaces of non-numbers?

• Autorzy: Kubica B.
• Konferencja: Evolutionary Computation and Global Optimization 2008 / National Conference (11 ; 2-4.06.2008 ; Szymbark, Poland)
• Języki publikacji: EN

Abstrakty

EN

Interval methods proved to be a useful tool for solving global optimization and nonlinear equations systems problems over Rn. But an interval may be defined not only over the set of real numbers or real vectors, but over any partially ordered set. The paper shows how basic ideas of interval computations can be generalized for such spaces. Some specific applications are proposed and preliminary computational results are presented.

Słowa kluczowe

EN

interval computations; global optimization

PL

przedział obliczeń; optymalizacja globalna

• Wydawca: Oficyna Wydawnicza Politechniki Warszawskiej
• Czasopismo: Prace Naukowe Politechniki Warszawskiej. Elektronika
• Rocznik: 2008
• Tom: z. 165
• Strony: 103--112
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Kubica B.

• Warsaw University of Technology, Institute of Control and Computation Engineering, ul. Nowowiejska 15/19, 00-065 Warsaw, Poland,

Bibliografia

• [1] K.R. Apt, "The Essence of Constraint Propagation", Theoretical Computer Science, Vol. 221, No. 1-2 (1999), pp. 179-210.
• [2] K.R. Apt, P. Zoeteweij, "An Analysis of Arithmetic Constraints on Integer Intervals", 2005; available on the web at http://homepages.cwi.nl/~apt/ps/az04-full. ps
• [3] E. Gardenes, M.A. Sainz, L. Jorba, R. Calm, R. Estela, R. Mielgo, A. Trepat, "Modal Intervals". Reliable Computing, Vol. 7, No. 2 (2001), pp. 77-111.
• [4] M.W. Gutowski, "Interval straight line fitting", 2001; available on the web at http://arxiv.org/pdf/math.NA/0108163
• [5] E. Kaucher, "Interval analysis in the extended interval space IR", Computing Supplement, No. 2 (1980), pp. 33-49.
• [6] R.B. Kearfott, M.T. Nakao, A. Neumaier, S.M. Rump, S.P. Shary, P. van Hentenryck. "Standardized notation in interval analysis", available on the web at http://www.mat.univie.ac.at/~neum/software/int/notation.ps.gz
• [7] B.J. Kubica, "Interval random variables and their application in queueing systems with long-tailed service times", Proceedings of The Third International Workshop on Soft Methods in Probability and St.atistics 2006, Bristol, U.K., Springer, 2000.
• [8] V.M. Nesterov, "Interval and Twin Arithmetics", Reliable Computing, Vol. 3 (1997), pp. 369-380.
• [9] I.A. Sharaya. "On Maximal Inner Estimation of the Solution Sets of Linear Systems with Interval Parameters", Reliable Computing, Vol. 7, No. 5 (2001), pp. 409-424.
• [10] S. Shary, "Algebraic approach to the interval linear static identification, tolerance and control problems, or One more application of Kaucher arithmetic", Reliable Computing, Vol. 2, No. l (1996), pp. 3-33.
• [11] M. Warmus, "Calculus of Approximations", Bulletin de l'Academie Polonaise de Sciences, Vol. 4, No. 5 (1956), pp. 253-257.
• [12] Wikipedia web page, "Interval (mathematics)", http://en.wikipedia.org/wiki/ Interval_%28mathematics%29