Geodesic
Rigorous global optimization of system parameters
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 2 (2014), pp. 61-71 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, after reviewing the basics of the method of Taylor models which enables rigorous computations, we introduced various function range bounding methods utilizing the inherent information associated to Taylor models. The superb performance is demonstrated by using a simple but tricky example. These components allow the construction of rigorous global optimization tools. We explain how to construct such a tool based on the branch-and-bound approach using the example function, while illustrating the excellent quality obtained by the method of Taylor models with this, we proceed to demonstrate the efficiency by applying the method to a practical application to search all the parameter operation points yielding desired properties in a lattice of a charged particle storage ring. Bibliogr. 14. Il. 3. Tabl. 2.
Keywords: rigorous computation, Taylor model, function range bound, rigorous global optimization, parameter optimization. 
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K. Makino; M. Berz. Rigorous global optimization of system parameters. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 2 (2014), pp. 61-71. http://geodesic.mathdoc.fr/item/VSPUI_2014_2_a6/

[1] Poklonskiy A., Evolutionary Optimization Methods for Beam Physics, PhD thesis, Michigan State University, East Lansing, Michigan, USA, 2009 http://bt.pa.msu.edu/pub

[2] Moore R. E., Interval Analysis, Prentice-Hall, Englewood Cliffs, New Jersey, 1966, 145 pp. | MR | Zbl

[3] Moore R. E., Methods and Applications of Interval Analysis, SIAM, Philadelphia, 1979, 201 pp. | MR | Zbl

[4] Alefeld G., Herzberger J., Introduction to Interval Computations, Academic Press, New York–London, 1983, 352 pp. | MR | Zbl

[5] Makino K., Rigorous Analysis of Nonlinear Motion in Particle Accelerators, PhD thesis, Michigan State University, East Lansing, Michigan, USA, 1998 ; MSUCL-1093, http://bt.pa.msu.edu/pub | Zbl

[6] Makino K., Berz M., “Taylor models and other validated functional inclusion methods”, Intern. Journal of Pure and Applied Mathematics, 6:3 (2003), 239–316 | MR | Zbl

[7] Makino K., Berz M., “Efficient control of the dependency problem based on Taylor model methods”, Reliable Computing, 5:1 (1999), 3–12 | DOI | MR | Zbl

[8] Berz M., Makino K., COSY INFINITY Version 9.1 programmer's manual, technical report MSUHEP-101214, Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan, USA, 2011 http://cosyinfinity.org

[9] Makino K., Berz M., “COSY INFINITY version 9”, Nuclear Instruments and Methods, 558 (2006), 346–350 | DOI

[10] Berz M., Modern Map Methods in Particle Beam Physics, Academic Press, San Diego, 1999 http://bt.pa.msu.edu/pub

[11] Berz M., “Forward algorithms for high orders and many variables”, Automatic Differentiation of Algorithms: Theory, Implementation and Application, SIAM, 1991, 147–156 | MR | Zbl

[12] Berz M., Makino K., Kim Y.-K., “Long-term stability of the Tevatron by validated global optimization”, Nuclear Instruments and Methods, 558 (2006), 1–10 | DOI

[13] Makino K., Berz M., “Range bounding for global optimization with Taylor models”, Transactions on Computers, 4:11 (2005), 1611–1618

[14] Robin D., Wan W., Sannibale F., “Global analysis of all linear stable settings of a storage ring lattice”, Phys. Review ST-AB, 11 (2008), 024002