Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2019, Volume 23, Number 2, Pages 361–377
Mathematical Modeling, Numerical Methods and Software Complexes
Effective computational procedure of the alternance optimization method
M. Yu. Livshits, A. V. Nenashev
Samara State Technical University, Samara, 443100, Russian Federation
The article discusses the computational procedure of the alternance optimization method as applied to the problem of semi-infinite programming. These problems are reduced numerous applied problems of optimization of objects with distributed and lumped parameters: robust parametric optimization of dynamic systems, parametric synthesis of control systems, etc. Since the calculation of alternance optimization method is rather difficult, as reduced to the solution, as a rule, the transcendental system of constitutive equations is proposed for efficient computational complexity of an embodiment of a computational procedure.
To reduce the complexity of the computational procedure, the properties of the extremum points of the optimality criterion established in the alternance method are used in the region of permissible values of variables. These properties allow creating a topology of this area and thereby minimizing the number of references to it during the search procedure. The proposed computational method is especially effective for non-convex and nonsmooth optimality criteria, to which the technologically sound statements of semiinfinite optimization result.
A step-by-step algorithm for preparing data and performing calculations, suitable for implementation in most programming languages, has been developed. The efficiency of the algorithm, which is higher, the larger the number of parameters included in the control vector and the higher the dimension of the optimization domain, is investigated. An estimate of the computational complexity of the computational procedure of the alternance optimization method is proposed, which makes it possible to determine the effectiveness of the application of the proposed algorithm for solving the problem of optimal control of the technological control object.
mathematical programming, nonconvex problem, optimal control, parameterization, search procedure
PDF file (944 kB)
(published under the terms of the Creative Commons Attribution 4.0 International License)
MSC: 65K05, 93B40
Received: March 13, 2019
Revised: May 14, 2019
Accepted: June 10, 2019
First online: July 3, 2019
M. Yu. Livshits, A. V. Nenashev, “Effective computational procedure of the alternance optimization method”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 23:2 (2019), 361–377
Citation in format AMSBIB
\by M.~Yu.~Livshits, A.~V.~Nenashev
\paper Effective computational procedure of the alternance optimization method
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
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