THE PROBLEM OF MINIMIZATION OF AN UNEVEN FUNCTION OF SEVERAL VARIABLES IN THE NORM l1 AND l∝ BY MEANS OF NEURAL NETWORKS (ENVIRONMENT. TECHNOLOGY. RESOURCES. Proceedings of the International Scientific and Practical Conference, 2005)
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.