Some directions and results of research in mathematical programming and system analysis. (English. Russian original) Zbl 0849.90127
Cybern. Syst. Anal. 31, No. 3, 317-349 (1995); translation from Kibern. Sist. Anal. 1995, No. 3, 3-48 (1995).
Summary: This article reviews the research in informatics, optimization theory, and system analysis associated with the scientific interests of our well-known scientist and mathematician, V. S. Mikhalevich, and his closest students and followers. We should qualify at the outset that the article does not review the full body of work of Mikhalevich, and certainly not of all his students: their work is much too extensive and much too multifaceted for one survey article. Moreover, in optimization theory, for instance, the Kiev mathematical school includes directions represented by other widely known scientists, and again these are not treated in the present article. I have decided to focus only on the studies and the directions of research to which V. S. Mikhalevich attached particular significance, which to a certain extent characterize his scientific creativity, and which are widely acknowledged among experts in our country and abroad.
The active development of research in mathematical programming and system analysis at the National Academy of Sciences of Ukraine began in the later 1950s and early 1960s, when the Computational Center of the Academy of Sciences of the Ukrainian SSR and a number of other scientific organizations in the country focused on the creation of new computers and computer software. At that time, Academician V. M. Glushkov organized in Kiev a number of scientific seminars, which served as a starting point for studies in optimization theory, modeling of production processes, and computer-aided design of complex objects. Glushkov was apparently among the first cybernetics who called attention to the need for the development of methods of system analysis, whose application in conjunction with modern computers to the study of complex processes in economics, medicine, engineering, and military science might achieve the desired goals. At that time, Mikhalevich himself, as well as his students and followers, were beginning their systematic work in this field. Their work was typically motivated by practical needs, and therefore immediately found wide applications for the solution of real-life problems.
The studies reviewed in this article can be classified into three main groups: (a) development and application of numerical optimization methods; (b) informatization of society and issues of economic cybernetics; (c) development of multiprocessor computers and computer software.
The active development of research in mathematical programming and system analysis at the National Academy of Sciences of Ukraine began in the later 1950s and early 1960s, when the Computational Center of the Academy of Sciences of the Ukrainian SSR and a number of other scientific organizations in the country focused on the creation of new computers and computer software. At that time, Academician V. M. Glushkov organized in Kiev a number of scientific seminars, which served as a starting point for studies in optimization theory, modeling of production processes, and computer-aided design of complex objects. Glushkov was apparently among the first cybernetics who called attention to the need for the development of methods of system analysis, whose application in conjunction with modern computers to the study of complex processes in economics, medicine, engineering, and military science might achieve the desired goals. At that time, Mikhalevich himself, as well as his students and followers, were beginning their systematic work in this field. Their work was typically motivated by practical needs, and therefore immediately found wide applications for the solution of real-life problems.
The studies reviewed in this article can be classified into three main groups: (a) development and application of numerical optimization methods; (b) informatization of society and issues of economic cybernetics; (c) development of multiprocessor computers and computer software.
MSC:
| 90C99 | Mathematical programming |
| 01A72 | Schools of mathematics |
| 01A65 | Development of contemporary mathematics |
References:
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| [126] | A. A. Chikrii, ”Variable direction method in nonlinear differential pursuit-and-evasion games,” Kibernetika, No. 1, 48–54 (1984). |
| [127] | A. A. Chikrii, ”A discrete search game with moving objects,” Dokl. Akad. Nauk UkrSSR, No. 10, 74–77 (1984). |
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| [130] | V. S. Mikhalevich, Yu. M. Kanygin, and V. I. Gritsenko, ”Informatics – a new field of science and practice,” in: Cybernetics. The Establishment of Informatics [in Russian], Nauka, Moscow (1986), pp. 31–45. |
| [131] | V. S. Mikhalevich, V. I. Skurikhin, Yu. M. Kanygin, and V. I. Grisenko, Some Approaches to the Conception of Informatization of Society [in Russian], Preprint 88-66, Inst. Kibern. im. V. M. Glushkov AN UkrSSR, Kiev (1988). |
| [132] | V. S. Mikhalevich, M. V. Mikhalevich, and I. V. Podolev, Modeling of Some Processes in Ukrainian Economy [in Russian], Preprint 93-46, Inst. Kibern. im. V. M. Glushkov AN UkrSSR, Kiev (1993). |
| [133] | V. S. Mikhalevich, M. V. Mikhalevich, and I. V. Podolev, Modeling of Some Mechanisms of Government Price Intervention in a Transition Economy [in Russian], Preprint 94-18, Inst. Kibern. im. V. M. GlushkovXA*p2175XUkrS Kiev (1994). |
| [134] | V. S. Mikhalevich, A. A. Bakaev, V. I. Gritsenko, V. L. Revenko, and Yu. N. Kuznetsov, Information Technology in Transportation. Railroad Transport [in Russian], Naukova Dumka, Kiev (1991). |
| [135] | A. A. Bakaev, V. I. Gritsenko, and V. L. Ravenko, Information Technology in Transportation. Water Transport [in Russian], Naukova Dumka, Kiev (1992). |
| [136] | I. V. Sergienko, V. S. Deineka, and V. V. Skopetskii, ”Solution of nonlinear parabolic equations with discontinuity in convective transport terms,” Dop. AN Ukrainy, Ser. A, No. 9, 21–24 (1989). · Zbl 0693.65079 |
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| [138] | I. V. Sergienko, V. V. Skopetskii, and V. S. Deineka, ”Some problems of computer-aided analysis of complex physical fields,” in: Application Software Packages [in Russian] Nauka, Moscow (1989), pp. 45–54. · Zbl 0850.76696 |
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| [142] | Yu. N. Onopchuk and D. I. Marchenko, ”Mathematical models of nitrogen saturation of the tissues of the human organism in case of hyperbaria,” Kibern. Vychisl. Tekhn., No. 63, 101–104 (1984). |
| [143] | E. A. Akhlamov, D. I. Marchenko, and Yu. N. Onopchuk, ”Modeling of the gas-exchange function of respiratory modes of the lungs with natural ventilation,” Kibern. Vychisl. Tekhn., No. 78, 67–71 (1988). |
| [144] | M. V. Bondarenko and Yu. N. Onopchuk, ”Mathematical aspects of the decompression problem,” in: Medical-Biological Topics in Decompression: Proc. 1 st All-Union Conf., Moscow, March 26–28, 1991 [in Russian], Inst. Med.-Biol. Problem, Moscow (1991), pp. 85–89. |
| [145] | V. S. Mikhalevich, V. M. Janenko, and K. L. Atoev, ”System analysis of organism’s defensive functions regulation (MODFR),” in: Selected topics on Mathematical Models in Immunology and Medicine: Proc. Intern. Workshop, Kiev, Aug. 28-Sept. 7, 1989, IIASA, Luxenburg (1990), pp. 137–146. |
| [146] | V. M. Janenko and K. L. Atoev, ”Mathematical simulation of the immunomodulating role of energy metabolism in support of synergism and antagonism of compartments of an immune system,” Acta Appl. Math.,14, 167–178 (1989). · Zbl 0677.92003 · doi:10.1007/BF00046683 |
| [147] | V. S. Mikhalevich, V. M. Yanenko, K. L. Atoev, et al., Mathematical Modeling of Regulatory Mechanisms of the Immune Systems Conditioned by Adenylic Acid 2’–5’ Oligonucleotides [in Russian], Preprint 90-47, Inst. Kibern. im. V. M. Glushkov AN UkrSSR, Kiev (1990). |
| [148] | V. S. Mikhalevich, V. M. Yanenko, and K. L. Atoev, ”The hierarchic mathematical model for risk estimation of ecological catastrophes,” Proc. Soc. for Risk Analysis, 1992 Annual Meeting, San Diego, Ca., December 6–9, 1992 (1992), pp. 1–4. |
| [149] | V. S. Mikhalevich, V. M. Yanenko, and K. L. Atoev, ”An information system for risk assessment of ecological catastrophes,” in: Modeling and Control of the Functional State of the Organism [in Russian], Inst. Kibern. im. V. M. Glushkov AN Ukr., Kiev (1993), pp. 52–74. |
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| [151] | M. Z. Zgurovskii, A. M. Demchenko, A. I. Novikov, and I. I. Kovalenko, System Analysis for the Study of Complex Physical Processes and Fields [in Russian], Preprint 93-30, Inst. Kibern. im. V. M. Glushkov AN Ukr., Kiev (1993). |
| [152] | M. Z. Zgurovskii and A. I. Novikov, ”System analysis of stochastic parallelized processes,” in: Modeling, State Estimation, and Identification [in Russian], Kiev. Politekhn. Inst., Kiev (1988). |
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| [158] | S. I. Lyashko, ”On solvability of mixed boundary-value problems with operator coefficients,” Usp. Mat. Nauk.,255, No. 2, 191–192 (1987). |
| [159] | S. I. Lyashko, ”Numerical methods of solution of optimal impulse control problems,” Zh. Vychisl. Matem. Mat. Fiz.,27, No. 43, 470–475 (1987). · Zbl 0623.65071 |
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| [161] | A. M. Gupal and A. M. Tsvetkov, ”Development of algorithms for inductive derivation of knowledge using decision leaves and trees,” USiM, No. 5/6, 21–26 (1992). |
| [162] | V. S. Mikhalevich, I. V. Sergienko, V. A. Trubin, et al., ”PLANER: an application software package for solving large production-transportation planning problems,” Kibernetika, No. 3, 57–71 (1983). |
| [163] | V. S. Mikhalevich, A. A. Bakaev, Yu. M. Ermol’ev, et al., A Software Package for Solving Transportation Problems. Solvable Problems, Features, and Source Language [in Russian], Preprint 81-40, Inst. Kibern. AN UkrSSR, Kiev (1981). |
| [164] | V. S. Mikhalevich, Yu. M. Ermol’ev, V. T. Loskutov, et al., ”Description of a software package for nondifferentiable and stochastic optimization,” in: Operations Research and MIS [in Russian], No. 27, Vishcha Shkola, Kiev (1986), pp. 1–19. |
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| [170] | I. N. Molchanov, An Introduction to Parallel Algorithms [in Russian], Naukova Dumka, Kiev (1990). |
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| [174] | V. S. Mikhalevich, Yu. V. Kapitonova, and A. A. Letichevskii, ”On methods of organization of macropipelined computation,” Kibernetika, No. 3, 3–10 (1986). |
| [175] | A. A. Letichevsky, V. S. Mikhalevich, and J. V. Kapitonova, ”On models of macroconveyor computation,” Information Processing ’86, Proc. World IFIP Congr., Elsevier (1986). |
| [176] | Yu. V. Kapitonova and A. A. Letichevskii, Mathematical Theory of Computer System Design [in Russian], Nauka, Moscow (1988). |
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| [178] | V. S. Mikhalevich and V. M. Kuntsevich, An Approach to the Analysis of the Arms Level Control Process [in Russian], Inst. Kibern. im. V. M. Glushkov AN UkrSSR, Kiev (1989). |
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