Abstract
Two problems of finding optimal parameters for multilayer optical coatings are considered. They are formulated as multiextremal nonlinear programming problems with a complex objective function. Finding local extrema by first-order methods is discussed. The ways of calculating the gradient of the objective function depending on the number of layers in the optical coating are analyzed.
Similar content being viewed by others
REFERENCES
Sh. A. Furman and A. V. Tikhonravov, Basics of Optics of Multilayer Systems, Gif-sur Yvette, Editions Frontiers (1992).
N. Z. Shor, Minimization Methods for Nondifferentiable Functions and their Applications [in Russian], Naukova Dumka, Kiev (1979).
N. Z. Shor, Nondifferentiable Optimization and Polynomial Problems, Kluwer Academ. Publ., Boston-Dordrecht-London (1998).
P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization, Acad. Press, New York (1981).
Yu. E. Nesterov, Efficient Methods in Nonlinear Programming [in Russian], Radio i Svyaz', Moscow (1989).
E. Polak, Computational Methods in Optimization, Acad. Press, New York (1971).
B. T. Polyak, Introduction to Optimization [in Russian], Nauka, Moscow (1983).
B. N. Pshenichnyi and Yu. M. Danilin, Numerical Methods in Extremum Problems [in Russian], Nauka, Moscow (1975).
D. M. Himmelblau, Applied Nonlinear Programming, McGraw Hill, New York (1972).
N. Z. Shor, N. G. Zhurbenko, A. P. Likhovid, and P. I. Stetsyuk, “Algorithms of nondifferentiable optimization: Development and application,” Cyb. Syst. Anal., Vol. 39, No.4, 537–548 (2003).
O. V. Mitsa and P. I. Stetsyuk, “The problem of finding optimal parameters of a uniform optic coating,” in: Theory of Optimal Solutions [in Russian], Inst. Kibern. im. V. M. Glushkova NAN Ukrainy, Kiev (2003), pp. 127–134.
Author information
Authors and Affiliations
Additional information
The study was performed within the framework of the Grant of the President of Ukraine for gifted youth, No. 19 (Executive Order of January 12, 2004, No. 6/2004-pr).
__________
Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 107–115, July–August 2005.
Rights and permissions
About this article
Cite this article
Stetsyuk, P.I., Mitsa, A.B. Parameter Optimization Problems for Multilayer Optical Coatings. Cybern Syst Anal 41, 564–571 (2005). https://doi.org/10.1007/s10559-005-0092-x
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10559-005-0092-x