Geodesic
Linear programming and dynamics
Ural mathematical journal, Tome 1 (2015) no. 1, pp. 3-19 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, Stability.
Mots-clés : Convergence 
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Anatoly S. Antipin; Elena V. Khoroshilova. Linear programming and dynamics. Ural mathematical journal, Tome 1 (2015) no. 1, pp. 3-19. http://geodesic.mathdoc.fr/item/UMJ_2015_1_1_a0/

[1] Eremin I.I., Mazurov Vl.D., Astafjev N.N., Improper problems of linear and convex programming, Nauka, Moscow, 1983, 336 pp. (in Russian)

[2] Eremin I.I., Conflicting models of optimal planning, Nauka, Moscow, 1988, 160 pp. (in Russian)

[3] Eremin I.I, “Duality for Pareto-successive linear optimization problems”, Trudy Inst. Mat. i Mekh. UrO RAN, 3, 1995, 245–260 | MR | Zbl

[4] Eremin I.I., The theory of linear optimization, UrO RAN, Ekaterinburg, 1999, 312 pp. (in Russian)

[5] Eremin I.I., Mazurov V.D., Questions of optimization and pattern recognition, Sredne-Ural. knizh. izd-vo, Sverdlovsk, 1979, 64 pp. (in Russian)

[6] Eremin I.I., The theory of duality in linear optimization, Publishing house YUUrGU, Chelyabinsk, 2005, 195 pp. (in Russian)

[7] Vasiliev F.P., Methods of optimization, in 2 bks., v. 1, 2, MTsNMO, Moscow, 2011, 620 pp. (in Russian)

[8] Kolmogorov A.N., Fomin S.V., Elements of the theory of functions and functional analysis, FIZMATLIT, Moscow, 2009, 572 pp. (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, 34:3 (2010), 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, 3 (2010), 2–20

[11] Vasiliev F.P., Khoroshilova E.V., Antipin A.S., “Regularized extragradient method for finding a saddle point in optimal control problem”, Proc. Steklov Inst. Math., 275, Suppl. 1. (2011), S186–S196

[12] Antipin A.S., “Two-person game with Nash equilibrium in optimal control problems”, Optim. Lett., 6:7 (2012), 1349–1378

[13] Khoroshilova E.V., “Extragradient method of optimal control with terminal constraints”, Autom. Remote Control, 73:3 (2012), 517–531 | DOI

[14] Khoroshilova E.V., “Extragradient-type method for optimal control problem with linear constraints and convex objective function”, Optim. Lett., 7:6 (2013), 1193–1214

[15] Antipin A.S., “Terminal Control of Boundary Models”, Comput. Math. Math. Phys., 54:2 (2014), 257–285

[16] Antipin A.S., Khoroshilova E.V., “On boundary value problem of terminal control with quadratic quality criterion”, Izvestiya IGU. Seriya: Matematika, 8 (2014), 7–28

[17] Antipin A.S., Vasilieva O.O., “Dynamic method of multipliers in terminal control”, Comput. Math. Math. Phys, 55:5 (2015), 766–787

[18] Antipin A.S., Khoroshilova E.V., “Optimal Control with Connected Initial and Terminal Conditions”, Proc. Steklov Inst. Math. (Suppl.), 289, suppl. 1 (2015), S9–S25 | DOI

[19] Konnov I.V., Equilibrium Models and Variational Inequalities, Mathematics in Science and Engineering, 210, Amsterdam, 2007, 248 pp.