The "Second Derivative" of a Non-Differentiable Function and its Use in Interval Optimization Methods

• Autorzy: Kubica B. J.
• Języki publikacji: EN

Abstrakty

EN

The paper presents an idea to use weak derivatives in interval global optimization. It allows using the Newton operator to narrow domains of non-differentiable functions. Preliminary computational experiments are also presented.

Słowa kluczowe

EN

Dirac delta; distributions; generalized derivative; interval computations; interval Newton method; nondifferentiable optimization

• Wydawca: Instytut Łączności - Państwowy Instytut Badawczy
• Czasopismo: Journal of Telecommunications and Information Technology
• Rocznik: 2011
• Tom: nr 4
• Strony: 81--85
• Opis fizyczny: Bibliogr. 8 poz., tab.

Twórcy

autor

Kubica B. J.

• Institute of Control and Computation Engineering, Warsaw University of Technology, Nowowiejska 15/19, 00-665 Warsaw, Poland,

Bibliografia

• [1] R. B. Kearfott, Rigorous Global Search: Continuous Problems. Dordrecht: Kluwer, 1996.
• [2] E. Hansen and W. Walster, Global Optimization Using Interval Analysis. New York: Marcel Dekker, 2004.
• [3] L. Jaulin, M. Kieffer, O. Didrit and E. Walter, Applied Interval Analysis. London: Springer, 2001.
• [4] R. B. Kearfott, M. T. Nakao, A. Neumaier, S. M. Rump, S. P. Shary and P. van Hentenryck, “Standardized notation in interval analysis” [Online]. Available: http://www.mat.univie.ac.at/∼neum/software/int/notation.ps.gz
• [5] M. J. Lighthill, Introduction to Fourier Analysis and Generalised Functions. Cambridge University Press, 1959.
• [6] H. Marcinkowska, Dystrybucje i Przestrzenie Sobolewa. Wrocław: Wydawnictwo Uniwersytetu Wrocławskiego, 1990 (in Polish).
• [7] V. S. Vladimirov, Methods of the Theory of Generalized Functions. Taylor & Francis, 2002.
• [8] C-XSC library [Online]. Available: http://www.xsc.de