A combined optimization algorithm analogous to the method of steepest descent (not in one-dimensional spaces, but in subspaces with different dimensionalities) and the method of gradient search is proposed. The choice of subspaces in which the descent is made is determined by the absolute values of the coordinates of the gradient at the regular iteration points.
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Yu. S. Sysoev and V. Sh. Magdeev, "Method for measuring deviations from cylindrical shape in large-scale workpieces," Izmer. Tekhn., No. 11, 27–29 (1990); Measur. Techn., 33, No. 11, 1104–1108 (1990).
Yu. S. Sysoev, V. Sh. Magdeev, S. N. Shponarskaya, and I. Yu. Kartasheva, "Determination of the average cylinder for a nonuniform distribution of monitoring points on the surface of large cylindrical workpieces," Izmer. Tekhn., No. 11, 21–27 (1997); Measur. Techn., 40, No. 11, 1056–1064 (1997).
Yu. S. Sysoev V. V. Krivin, and V. G. Beketov, "Use of mixtures of distributions in stochastic identification of multivariant objects," Izmer. Tekhn., No. 6, 9–13 (2007); Measur. Techn., 50, No. 6, 575–580 (2007).
Yu. S. Sysoev, "Coordinate methods for monitoring the geometry of the surfaces of machine building workpieces (spatial methods for monitoring the surfaces of machined parts): A Handbook," Inzh. Zh., No. 5, 16–22 (2007).
J. Dennis and R. Schnabel, Numerical Methods for Unconditional Optimization and Solution of Nonlinear Equations [Russian translation], Mir, Moscow (1988).
D. Himmelblau, Applied Nonlinear Programming [Russian translation], Mir, Moscow (1975).
Yu. S. Sysoev, V. Sh. Magdeev, and E. P. Voronin, "Study of the perception of text information from luminous explosion-protected panels by subjective measurement methods," Pozharovzryvobezopasnost, No. 6, 443–49 (2012).
T. Saaty, Decision Making. The Analytic Hierarchy Process [Russian translation], Radio i Svyaz, Moscow (1993).
Yu. S. Sysoev, I. Yu. Gil't, and S. M. Vinnichenko, "The optimal group strategy method for matching subjective measurements," Izmer. Tekhn., No. 2, 20–22 (2006); Measur. Techn., 49, No. 2, 122–126 (2006).
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Translated from Izmeritel'naya Tekhnika, No. 4, pp. 9–12, April, 2015.
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Sysoev, Y.S. Combined Optimization Algorithm and its Applications in Metrology. Meas Tech 58, 376–380 (2015). https://doi.org/10.1007/s11018-015-0720-4
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DOI: https://doi.org/10.1007/s11018-015-0720-4