THE PROBLEM OF MINIMIZATION OF AN UNEVEN FUNCTION OF SEVERAL VARIABLES IN THE NORM l1 AND l∝ BY MEANS OF NEURAL NETWORKS

Józef Gil

Abstract


The paper presents the problem of the minimization of an uneven function of several variables F: Rm →Rn . In general, the minimization of an uneven function is difficult in terms of numerical application, especially when there is no information about the character of the unevenness of the function or any precise data about the distribution of observation errors. This paper presents two algorithms for the minimization of an uneven function by means of neural networks: solutions to an overdetermined system of linear equations according to the criteria of the norm l1 and according to the criteria of the norm l∝ (the Chebyshev norm) with the use of a square and exact penalty function. The results of particular solutions have been compared with the solution via the method of the least squares. The equalization tasks have been performed with minimum restrictions of extents of freedom.


Keywords


minimization of an uneven function in the norm 1l and l∝

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References


Brillou in L., Nauka a teoria informacji, PWN, Warszawa 1969.

Cichocki A., Unbehauen R., Neural Networks for Solving Systems of Linear Equations – Part II:minimax and Least Absolute Value Problems, IEEE Transactions on Circuits and Systems, Vol. 39, No.9, 1992.

Dahlquist G., Björck Ä., Metody numeryczne, PWN, Warszawa 1983.

Fletcher R., Practical Methods of Optimization. New York: Wiley-Interscience, 1986.

Huber P.,J., Robust Statistics, New York:Wiley, 1981.

Kadaj R., Modele, metody i algorytmy obliczeniowe sieci kinematycznych w geodezyjnych pomiarach przemieszczeń i odkształceń obiektów, monografia, Wydawnictwo A R im. H. Kołłątaja w Krako wie, Kraków 1998.

Kennedy M.P., Chua L.O., Neural networks for nonlinear programming, IEEE Trans. Circu its Syst., vol. CAS-34, 1987.

Korn Granino,A., Korn Teresa, M., Matematyka dla pracowników naukowych i in żynieró w, cz. II, PWN, Warszawa 1983.

Nowak E., Badanie przemieszczeń drogą statystycznej weryfikacji poprawności modelu i obserwacji, Mat. Sympozjum „Informatyka w Geodezji”, Warszawa 1982.




DOI: http://dx.doi.org/10.17770/etr2005vol1.2125

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