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Trudy Inst. Mat. i Mekh. UrO RAN, 2016, Volume 22, Number 2, Pages 71–78 (Mi timm1292)  
Extragradient method for finding a saddle point in a multicriteria problem with dynamics

F. P. Vasil'eva, A. S. Antipinb, L. A. Artem'evaa

a Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
b Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow

Abstract: We consider an optimal control problem for a linear system of ordinary differential equations with an implicitly given boundary condition connected with a multicriteria problem. Such problems arise, for example, in the study of controlled objects that lose their stability under the influence of external perturbations, where it is required to return the object to stability by means of an appropriate choice of the control. We describe a possible mathematical model of this kind, propose an extragradient method for recovering the stability, and investigate its convergence.

Keywords: optimal control problem, Cauchy problem, multicriteria problem, saddle point, convergence.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-06045-а
Ministry of Education and Science of the Russian Federation 02.А03.21.0004


DOI: https://doi.org/10.21538/0134-4889-2016-22-2-71-78

Full text: PDF file (162 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2017, 297, suppl. 1, 203–210

Bibliographic databases:

UDC: 517.977
MSC: 37N40, 49J15, 49M30, 93C15, 90C29
Received: 24.02.2016

Citation: F. P. Vasil'ev, A. S. Antipin, L. A. Artem'eva, “Extragradient method for finding a saddle point in a multicriteria problem with dynamics”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 2, 2016, 71–78; Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 203–210

Citation in format AMSBIB
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\paper Extragradient method for finding a saddle point in a multicriteria problem with dynamics
\serial Trudy Inst. Mat. i Mekh. UrO RAN
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\vol 22
\issue 2
\pages 71--78
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