Geodesic
Regularized Extragradient Method of Finding a Solution to an Optimal Control Problem with Inaccurately Specified Input Data
Informatics and Automation, Optimal control and differential equations, Tome 304 (2019), pp. 137-148

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We consider an optimal control problem described by a system of linear ordinary differential equations with boundary conditions of general form defined by inequality-type constraints in the case when the input data are inaccurately specified. In general, such problems are unstable with respect to perturbations of the input data and require the development of special stable solution methods. In this paper we propose a regularized variant of the extragradient method, study its convergence, and construct a regularizing operator.
Keywords: optimal control problem, Lagrange function, Tikhonov function, saddle point, extragradient method, regularization method, regularizing operator. 
@article{TRSPY_2019_304_a7,
     author = {F. P. Vasil'ev and L. A. Artem'eva},
     title = {Regularized {Extragradient} {Method} of {Finding} a {Solution} to an {Optimal} {Control} {Problem} with {Inaccurately} {Specified} {Input} {Data}},
     journal = {Informatics and Automation},
     pages = {137--148},
     publisher = {mathdoc},
     volume = {304},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2019_304_a7/}
}
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F. P. Vasil'ev; L. A. Artem'eva. Regularized Extragradient Method of Finding a Solution to an Optimal Control Problem with Inaccurately Specified Input Data. Informatics and Automation, Optimal control and differential equations, Tome 304 (2019), pp. 137-148. http://geodesic.mathdoc.fr/item/TRSPY_2019_304_a7/