Geodesic
Dynamics and variational inequalities
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 5, pp. 783-800

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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. 
@article{ZVMMF_2017_57_5_a2,
     author = {A. S. Antipin and V. Ja\'cimovi\'c and M. Ja\'cimovi\'c},
     title = {Dynamics and variational inequalities},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {783--800},
     publisher = {mathdoc},
     volume = {57},
     number = {5},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_5_a2/}
}
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A. S. Antipin; V. Jaćimović; M. Jaćimović. Dynamics and variational inequalities. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 5, pp. 783-800. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_5_a2/