Abstract
From the beginning of the seventies the investigation on constructive theory of optimal control has been carried out under the guidance of the authors in Minsk (Institute of Mathematics of the BSSR Academy of Sciences; Byelorussian State University). Since then a number of new optimization algorithms have been worked out and tested by computer. At first static linear programming problems have been considered, then the suggested methods have been transferred on other mathematical programming problems and dynamic models. Now methods for solution of linear optimal control problems are investigated in detail and the first steps axe made towards constructing methods for solution of nonlinear problems. Below a survey of some results obtained by the members of Minsk Seminar on constructive optimal control methods is given and new algorithms of solving extremal problems are described.
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References
Gabasov, R.; Kirillova, P. M.: Linear programming methods. Minsk: BGU Publishing House, parts I-III, 172 p., 240 p., 368 p. (1977, 1978, 1980).
Gabasov, R.; Kirillova, P.M.: Methods of parametric and functional optimization. Preprints of IPAC 8th Triennial World Congress, Kyoto, Japan. IV, 111–116 (1981).
Gabasov, R.; Kirillova, P.M.; Lutov, A.I.; Senko, A.A.: New algorithms of solution of optimal control problems. In: Punctional-Diff. Systems and Related Topics. II. Proc. of the Second Intern. Conf. Poland, Blazejewko. 111–118 (1981).
Kirillova, P.M.; Kostyukova, O. I.; Gabasov, R.: Adaptive method for solving large problems of linear programming. Symposium Optimization Methods (applied aspects). Preprints of IPAC-IPOPS, Bulgaria. 163–170 (1979).
Gabasov, R.; Kirillova, P.M.: New methods of linear programming and their application to optimal control. Proc. IPAC Workshop on Appl. Non-linear Program., Denver, Pergamon-Press, 241–267 (1980).
Gabasov, R.(ed.); Kirillova, P.M. (ed.): Optimal control problems. Proc. of the Minsk Seminar on Optimal Control Problems. Minsk: Nauka i Technika. 370 p. (1981).
Gabasov, R.; Kirillova, P.M.; Glushenkov V.S., Senko, A.A.; Tyatyushkin, A.I: Algorithms of optimization of linear and nonlineax systems. Madrid: Proc. of the 3d IPAC/IPIP Symposium on Software for Computer Control. 333–338 (1982).
Gabasov, R.; Kirillova, P.M.; Tyatyushkin, A.I.: Constructive optimization methods. P.1. Linear systems. Minsk: BGU Publishing House, (to appear).
Gabasov R.; Kirillova, P.M.: Constructive methods of solving extremal problems. Poland: Preprints of 3d Polish-English Seminar on Real-Time Processes. 83–95 (1980).
Gabasov, R.; Kirillova, P.M.; Kostyukova, O.I.: Pinite primal exact linear programming algorithm. 25, 301–304,1981.
Danzig, J.: Linear programming, its generalizations and applications. Moscow: Progress. 600 p. (1966).
Charnes, A.; Granot, D.; Granot, G.: A primal algorithm for interval linear programming problems. Linear algebra and its applications, 17. 1, 65–78 (1977).
Gabasov, R.; Kirillova, P.M.(ed.); Senko, A.A.(ed.): Programme package “Adaptive Optimization”. Minsk: Institute of Mathematics. 43. 239 p. (1983).
Senko A. A.: Algorithms for solution of an interval linear programming problem. Izvestiya AN BSSR. Ser. phys.-math. nauk, 5, 21–26 (1982).
Gabasov, R.; Kirillova, P.M.; Kostyukova, O.I.; Senko, A. A.: Two-phase methods of solving canonical linear programming problem. Doklady AN BSSR, 27, 787–790 (1983).
Gabasov, R.; Shilkina, E.I.: Primal exact method for solution of one class of minimax problems. Doklady AN BSSR, 25, 971–973 (1981).
Gabasov, R.; Kirillova, P.M.; Raketsky V.M.: On methods for solution of a general convex quadratic programming problem. Doklady AN SSSR, 258, 1289–1293 (1981).
Duffin, R.; Peterson, E.; Zener, C.: Geometric programming. Moscow: Mir. 311 p.(1972).
Pokatayev, A.V.: Algorithm for solution of unconstrained geometric programming problem. Izvestiya AN SSSR, Technicheskaya cibernetika, 1, 39–46, (1982).
Rijckaert, M. J.; Martens, X.M.: Comparison of generalized geometric programming algorithms. J. Optimiz. Theory and Appl., 26, 205–242 (1978).
Dembo, R.S.: A set of geometric programming test problems and their solutions. Math. Prog., 10, 192–213 (1976).
Gabasov, R.; Kirillova, P.M.; Kostyukova, O.I.: On construction of the first order algorithm for solution of optimal control problems. Doklady AN SSSR, 254, 562–566 (1980).
Gabasov, R.; Kirillova, P.M.; Kostyukova, O.I.: Primal exact algorithm for solution of a linear optimal control problem. Izvestiya AN SSSR. Technicheskaya cibernetika, 1, 68–75, (1982).
Gabasov, R.; Glushenkov, V.S.: Pinite μ-adaptive exact method for solution of a general linear programming problem. Doklady AN BSSR, 26, 589–592 (1982).
Gabasov, R.; Kirillova, P.M.; Gnevko, S.V.; Daukshas, V.Z.: Algorithms of optimal control of dynamic systems. In: Functional-Differential Systems and Related Topics. III. Proc. of the Third International Conference. Poland, 1983 (to appear).
Gabasov, R.(ed.); Kirillova, P.M.(ed.); Senko, A.A.(ed.): Programme package “Software. Adaptive optimization. II.” (to appear).
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Gabasov, R., Kirillova, F.M. (1984). New Algorithms and Results of Numerical Experiments for Solution of Mathematical Programming and Optimal Control Problems. In: Hammer, G., Pallaschke, D. (eds) Selected Topics in Operations Research and Mathematical Economics. Lecture Notes in Economics and Mathematical Systems, vol 226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45567-4_35
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DOI: https://doi.org/10.1007/978-3-642-45567-4_35
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