Abstract
The paper deals with a decomposition of a multivariate function into the summands of different dimensionality. The proposed methods of structure analysis enable to approximate the multidimensional function (the objective function in optimisation) by the functions of fewer variables. It is shown that step by step partition of the range of definition may be used to reduce the interactions of variables in the parts.
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Bibliography
Simon, H. A. and Ando, A.: Aggregation of variables in dynamic systems, Econometrica 29 (1964), 111–138.
Courtois, P.-J.: Decomposability, Academic Press, New York, 1977.
Courtois, P.-J.: On time and space decomposition of complex structures, Comm. ACM 28(6) (1985), 590–603.
Cukier, R. I., Levine, H. B. and Shuler, K. E.: Nonlinear sensitivity analysis of multiparameter model systems, J. Comput. Phys. 26(1) (1978), 1–42.
Šaltenis, V.: Structure Analysis of Optimisation Problems, Mokslas, Vilnius, 1989, 123 p. (in Russian).
Soboľ, I. M.: On sensitivity estimation for nonlinear mathematical models, Mat. Mod. 2(1) (1990), 112–118 (in Russian).
Soboľ, I. M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates, Math. Comput. Simulation 55 (2001), 271–280.
Golomb, M.: Approximation by functions of fewer variables, In: On Numerical Approximation. Proceedings of a Symposium, Conducted by the Mathematics Research Centre, R. E. Langer (ed.), The University of Wisconsin Press, Madison, 1959, pp. 275–327.
Šaltenis, V.: Analysis of multivariate function structure in classification problems, Informatica 7(4) (1996), 525–541.
Šaltenis, V.: Grid with uniformity adapted to the structure of a multidimensional problem, Informatica 8(4) (1997), 583–598.
Šaltenis, V.: Global sensitivity analysis of infection spread, radar search and multiple criteria decision models, Informatica 9(2) (1998), 235–252.
Dixon, L. C. W. and Cziego, G. P.: The Global Optimisation Problem: An Introduction, Towards Global Optimisation 2, North-Holland, Amsterdam, 1978, pp. 1–15.
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Šaltenis, V., Tiešis, V. (2002). The Structure of Multivariate Models and the Range of Definition. In: Dzemyda, G., Šaltenis, V., Žilinskas, A. (eds) Stochastic and Global Optimization. Nonconvex Optimization and Its Applications, vol 59. Springer, Boston, MA. https://doi.org/10.1007/0-306-47648-7_12
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DOI: https://doi.org/10.1007/0-306-47648-7_12
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4020-0484-1
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