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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, Issue 1, Pages 102–117 (Mi vuu420)  

This article is cited in 4 scientific papers (total in 4 papers)

MATHEMATICS

On applicability of control parametrization technique to solving distributed optimization problems

A. V. Chernovab

a Nizhni Novgorod State University, pr. Gagarina, 23, Nizhni Novgorod, 603950, Russia
b Nizhni Novgorod State Technical University, ul. Minina, 24, Nizhni Novgorod, 603950, Russia

Abstract: We study approximating finite-dimensional mathematical programming problems arising from piecewise constant discretization of the control (in the framework of control parametrization technique) in the course of optimization of distributed parameter systems of a rather wide class. We establish the Lipschitz continuity for gradients of approximating problems. We present their formulas involving analytical solutions of an original controlled system and their adjoint one, thereby giving the opportunity for algorithmic separation of the optimization problem itself and the problem of solving a controlled system. Application of the approach under study to numerical optimization of distributed systems is illustrated by example of the Cauchy–Darboux system controlled by an integral criterion. We present the results of numerical solving the corresponding approximation problem in MatLab with the help of the program {\tt fmincon} and also an author-developed program based on the conditional gradient method. Moreover, the unconstrained minimization problem is investigated that arises from the constrained approximation problem with applying the sine parametrization method. We present the results of numerical solving this problem in MatLab with the help of the program {\tt fminunc} and also two author-developed programs based on the steepest descent and BFGS methods, respectively. The results of all numerical experiments are analyzed in detail.

Keywords: distributed parameter systems optimization, functional differentiation, piecewise constant approximation of control, control parametrization technique.

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Document Type: Article
UDC: 517.957+517.988+517.977.56
MSC: 47J05, 47J35, 47N10, 49M25, 49M37
Received: 19.12.2013

Citation: A. V. Chernov, “On applicability of control parametrization technique to solving distributed optimization problems”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2014, no. 1, 102–117

Citation in format AMSBIB
\Bibitem{Che14}
\by A.~V.~Chernov
\paper On applicability of control parametrization technique to solving distributed optimization problems
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2014
\issue 1
\pages 102--117
\mathnet{http://mi.mathnet.ru/vuu420}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Chernov, “On total preservation of solvability for a controlled Hammerstein type equation with non-isotone and non-majorized operator”, Russian Math. (Iz. VUZ), 61:6 (2017), 72–81  mathnet  crossref  isi
    2. A. V. Chernov, “Ob ispolzovanii kvadratichnykh eksponent s variruemymi parametrami dlya approksimatsii funktsii odnogo peremennogo na konechnom otrezke”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:2 (2017), 267–282  mathnet  crossref  elib
    3. A. V. Chernov, “JPEG-like method of control parametrization for numerical solution of the distributed optimization problems”, Autom. Remote Control, 78:8 (2017), 1474–1488  mathnet  crossref  isi  elib
    4. A. V. Chernov, “O primenenii kvadratichnykh eksponent dlya diskretizatsii zadach optimalnogo upravleniya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:4 (2017), 558–575  mathnet  crossref  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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