LINEAR PROGRAMMING AND DYNAMICS

Anatoly S. Antipin     (Computing Center of RAS, Moscow, Russia, Russian Federation)
Elena V. Khoroshilova     (Lomonosov Moscow State University, Russian Federation)

Abstract


In a Hilbert space we consider the linear boundary value problem of optimal control based on the linear dynamics and the terminal linear programming problem at the right end of the time interval. There is provided a saddle-point method to solve it. Convergence of the method is proved.

Keywords


Linear programming; Optimal control; Boundary value problems; Methods for solving problems; Convergence; Stability

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References


  1. Eremin I.I., Mazurov Vl.D., Astafjev N.N. Improper problems of linear and convex programming. Moscow: Nauka, 1983. 336 p. (in Russian)
  2. Eremin I.I. Conflicting models of optimal planning. Moscow: Nauka, 1988. 160 p. (in Russian)
  3. Eremin I.I. Duality for Pareto-successive linear optimization problems // Tr. In-ta matematiki i mekhaniki UrO RAN. 1995. Vol. 3. P. 245-261 (in Russian)
  4. Eremin I.I. The theory of linear optimization. Ekaterinburg, Ekaterinburg, 1999. 312 p. (in Russian)
  5. Eremin I.I., Mazurov Vl.D. Questions of optimization and pattern recognition. Sverdlovsk, Sredne-Ural. knizh. izd-vo, 1979. 64 p. (in Russian)
  6. Eremin I.I. The theory of duality in linear optimization. Chelyabinsk: Publishing house YUUrGU, 2005. 195 p. (in Russian)
  7. Vasiliev F.P. Methods of optimization: in 2 bks. Bk. 1, 2. Moscow, MTsNMO, 2011. 620 p. (in Russian)
  8. Kolmogorov A.N., Fomin S.V. Elements of the theory of functions and functional analysis. Moscow: FIZMATLIT, 2009. (in Russian)
  9. Vasiliev F.P., Khoroshilova E.V., Antipin A.S. An Extragradient Method for Finding the Saddle Point in an Optimal Control Problem // Moscow University Comp. Maths. and Cybernetics. 2010. Vol. 34. no 3. P. 113-118.
  10. Antipin A.S., Khoroshilova E.V. On methods of extragradient type for solving optimal control problems with linear constraints // Izvestiya IGU. Seriya: Matematika. 2010. Vol. 3. P. 2-20 (in Russian)
  11. Vasiliev F.P., Khoroshilova E.V., Antipin A.S. Regularized extragradient method for finding a saddle point in optimal control problem // Proceedings of the Steklov Institute of Mathematics. 2011. Vol. 275, suppl. 1. P. 186-196.
  12. Antipin A.S. Two-person game with Nash equilibrium in optimal control problems // Optim. Lett. 2012. 6(7). P. 1349-1378.
  13. Khoroshilova E.V. Extragradient method of optimal control with terminal constraints // Automation and Remote Control. 2012. Vol. 73, no. 3. P. 517-531.
  14. Khoroshilova Elena V. Extragradient-type method for optimal control problem with linear constraints and convex objective function // Optim. Lett., August 2013. Vol. 7, iss. 6, P. 1193-1214.
  15. Antipin A.S. Terminal Control of Boundary Models // Comput. Math. Math. Phys. 2014. V. 54, no 2. P. 257-285.
  16. Antipin A.S., Khoroshilova E.V. On boundary value problem of terminal control with quadratic quality criterion // Izvestiya IGU. Seriya: Matematika. 2014. Vol. 8. P. 7-28.
  17. Antipin A.S., Vasilieva O.O. Dynamic method of multipliers in terminal control // Comput. Math. Math. Phys. 2015. Vol. 55, no 5. P. 766-787.
  18. Antipin A.S., Khoroshilova E.V. Optimal Control with Connected Initial and Terminal Conditions // Proceedings of the Steklov Institute of Mathematics. 2015. Vol. 289, suppl. 1. P. 9-25.
  19. Konnov I.V. Equilibrium Models and Variational Inequalities. Kazan State University, 2007 (in Russian)



DOI: http://dx.doi.org/10.15826/umj.2015.1.001

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