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Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 5, Pages 783–800 (Mi zvmmf10570)  

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

Dynamics and variational inequalities

A. S. Antipina, V. Jaćimovićb, M. Jaćimovićb

a Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Moscow, Russia
b Faculty of Mathematics and Natural Sciences, University of Montenegro, Podgorica, Montenegro

Abstract: A terminal control problem with linear dynamics and a boundary condition given implicitly in the form of a solution of a variational inequality is considered. In the general control theory, this problem belongs to the class of stabilization problems. A saddle-point method of the extragradient type is proposed for its solution. The method is proved to converge with respect to all components of the solution, i.e., with respect to controls, phase and adjoint trajectories, and the finite-dimensional variables of the terminal problem.

Key words: linear dynamics, control, boundary value problem, variational inequality, saddle-point method, convergence.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-06045_а
Ministry of Education and Science of the Russian Federation НШ-8860-2016.1


DOI: https://doi.org/10.7868/S0044466917050015

Full text: PDF file (189 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:5, 784–801

Bibliographic databases:

UDC: 519.626
Received: 01.05.2016

Citation: A. S. Antipin, V. Jaćimović, M. Jaćimović, “Dynamics and variational inequalities”, Zh. Vychisl. Mat. Mat. Fiz., 57:5 (2017), 783–800; Comput. Math. Math. Phys., 57:5 (2017), 784–801

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. S. Antipin, E. V. Khoroshilova, “Feedback synthesis for a terminal control problem”, Comput. Math. Math. Phys., 58:12 (2018), 1903–1918  mathnet  crossref  crossref  isi  elib
    2. F. S. Stonyakin, “An adaptive analog of Nesterov's method for variational inequalities with a strongly monotone operator”, Num. Anal. Appl., 12:2 (2019), 166–175  mathnet  crossref  crossref  isi  elib
    3. Yao Y., Postolache M., Yao J.-Ch., “Iterative Algorithms For Generalized Variational Inequalities”, Univ. Politeh. Buchar. Sci. Bull.-Ser. A-Appl. Math. Phys., 81:2 (2019), 3–16  isi
    4. F. S. Stonyakin, “Ob adaptivnom proksimalnom metode dlya nekotorogo klassa variatsionnykh neravenstv i smezhnykh zadach”, Tr. IMM UrO RAN, 25, no. 2, 2019, 185–197  mathnet  crossref  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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