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The Scientific Heritage of B. N. Pshenichnyi

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Cybernetics and Systems Analysis Aims and scope

Abstract

Pshenichnyi's achievements in the investigation of necessary extremum conditions, computational methods of optimization, and differential games are outlined at a qualitative level.

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REFERENCES

  1. B. N. Pshenichnyi, Necessary Conditions of Extremum [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  2. B. N. Pshenichnyi, Convex Analysis and Extremum Problems [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  3. V. F. Dem'yanov and A. M. Rubinov, “On quasidifferentiable subdifferentials,” DAN SSSR, 20, No. 4, 21-25 (1980).

    Google Scholar 

  4. H. Halkin and L. Neustadt, “General necessary conditions for optimization problems,” Proc. Nat. Acad. Sci. USA, 56, 1066-1071 (1966).

    Google Scholar 

  5. B. N. Pshenichnyi, “On the necessary conditions of extremum for nonsmooth functions,” Kibernetika, No. 6, 92-96 (1977).

  6. B. N. Pshenichnyi, “Convex multivalued mappings and mappings conjugate to them,” Kibernetiks, No. 3, 94-102 (1972).

  7. B. N. Pshenichnyi, “Theorems on implicit functions for multivalued mappings,” Kibernetika, No. 4, 36-43 (1986).

  8. V. M. Kuntsevich and B. N. Pshenichnyi, “Minimal invariant sets of dynamic systems with bounded disturbances, Kibern. Sist. Anal., No. 1, 74-81 (1996).

  9. V. M. Kuntsevich and B. N. Pshenichnyi, “Invariant and stationary sets of nonlinear discrete systems under bounded disturbances,” Probl. Upravl. Inform., No. 1-2, 35-45 (1996).

  10. V. M. Kuntsevich and B. N. Pshenichnyi, “Analysis of some classes of nonlinear discrete systems under bounded disturbances,” Proc. 4th IFAK Nonlinear Control Systems Design Symp., Amsterdam (1998), pp. 275-280.

  11. V. M. Kuntsevich and B. N. Pshenichnyi, “Solution of a class of pursuit and evasion problems under uncertainty,” Kibern. Sist. Anal., No. 3, 63-70 (1995).

  12. V. M. Kuntsevich, “Analysis and synthesis of optimal discrete control systems under bounded noise,” Kibern. Sist. Anal., No. 5, 1-27 (1996).

  13. V. M. Kuntsevich and A. V. Kuntsevich, “Analysis and synthesis of optimal and robustly optimal control systems under bounded disturbances,” Proc. 14th IFAC World Congress (Beijing, 1999), Vol. F, Nonlinear Systems I, Beijing (1999), pp. 163-168.

    Google Scholar 

  14. B. N. Pshenichnyi and E. E. Kirik, “Nonlinear programming methods and network flows,” Kibern. Sist. Anal., No. 6, 67-77 (1994).

  15. B. N. Pshenichnyi, “Design of power networks using electronic computers,” ZhVM MF, 2, No. 5, 942-947 (1962).

    Google Scholar 

  16. B. N. Pshenichnyi, “A numerical method for solving optimal control problems,” ZhVM MF, 2, No. 2, 281-287 (1964).

    Google Scholar 

  17. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, Mathematical Theory of Optimal Processes [in Russian], Fizmatgiz, Moscow (1961).

    Google Scholar 

  18. G. Kuhn and A. Tucker (eds.), Linear Inequalities and Adjacent Problems [Russian translation], Izd. Inostr. Lit., Mosvcow (1959).

    Google Scholar 

  19. A. Ya. Dubovitskii and A. A. Milyutin, “Extremum problems under constraints,” ZhVM MF, 5, No. 3, 395-453 (1965).

    Google Scholar 

  20. A. Ya. Dubovitskii and A. A. Milyutin, Necessary Conditions of Extremum in the General Problem of Optimal Control [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  21. I. V. Girsanov, Mathematical Theory of Extremum Problems [in Russian], Izd. MGU, Moscow (1970).

  22. E. G. Gol'shtein, Theory of Duality in Mathematical Programming [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  23. V. F. Dem'yanov and A. M. Rubinov, Approximate Methods of Solution of Extremum Problems [in Russian], Izd. LGU, Leningrad (1968).

    Google Scholar 

  24. A. D. Ioffe and V. L. Levin, Subdifferentials of convex functions," Tr. MMO, 26, 3-73 (1972).

    Google Scholar 

  25. A. D. Ioffe and V. M. Tikhomirov, Theory of Extremum Problems [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  26. B. N. Pshenichnyi, “Necessary conditions of extremum for differential inclusions,” Kibernetika, No. 6, 60-73 (1976).

  27. V. L. Makarov and A. M. Rubinov, Mathematical Theory of Economic Dynamics and Equilibrium [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  28. F. N. Clark, Optimization and Nonsmooth Analysis [Russian translation], Nauka, Moscow (1988).

    Google Scholar 

  29. G. Sh. Rubinshtein, “Dual extremum problems,” DAN USSR, 152, No. 2, 288-291 (1963).

    Google Scholar 

  30. B. N. Pshenichnyi and E. I. Nenakhov, “Necessary conditions of the minimum in problems with operator constraints,” Kibernetika, No. 3, 35-46 (1971).

  31. V. M. Glushkov and B. N. Pshenichnyi, “On a mathematical model of developing economy,” Kibernetika, No. 4, 1-6 (1977).

  32. B. N. Pshenichnyi, “Model of production and exchange,” Kibernetika, No. 4, 128-132 (1981).

  33. B. N. Pshenichnyi, E. I. Nenakhov, and V. N. Kuz'menko, “Mixed method for solving the general convex programming problem,” Kibern. Sist. Anal., No. 4, 121-134 (1998).

    Google Scholar 

  34. V. G. Boltyanskii, Optimal Control of Discrete Systems [in Russian], Nauka, Moscow (1973).

    Google Scholar 

  35. J. P. Aubin and I. Ekeland, Applied Nonlinear Analysis [Russian translation], Mir, Moscow (1988).

    Google Scholar 

  36. V. I. Arkin and V. L. Levin, “Convexity of the values of vector integrals, the theorem of measurable choice, and variational problems,” UMN, 27, No. 3, 21-77 (1972).

    Google Scholar 

  37. B. S. Morduhovich, Approximation Methods in Optimization and Control Problems [in Russian], Nauka, Moscow (1988).

    Google Scholar 

  38. I. V. Sergienko, Mathematical Models and Methods of Solving Discrete Optimization Problems [in Russian], Naukova Dumka, Kiev (1988).

    Google Scholar 

  39. I. V. Sergienko, Computer Science in Ukraine. Formation, Development, and Problems [in Ukrainian], Naukova Dumka, Kiev (1999).

    Google Scholar 

  40. V. S. Deineka, I. V. Sergienko, and V. V. Skopetskii, Models and Methods of Solving Problems with Conjugation Conditions [in Russian], Naukova Dumka, Kiev (1998).

    Google Scholar 

  41. V. S. Deineka and I. V. Sergienko, Models and Methods of Solving Problems in Inhomogeneous Media [in Russian],Naukova Dumka, Kiev (2001).

    Google Scholar 

  42. B. N. Pshenichnyi and V. S. Kirilyuk, “Theorems on implicit functions for multivalued mappings,” DAN USSR, Ser. A, No. 9, 77-79 (1986).

  43. L. S. Pontryagin, Selected Works [in Russian], Vol. 2, Nauka, Moscow (1988).

    Google Scholar 

  44. N. N. Krasovskii, Game Problems on Encounter of Motions [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  45. D. L. Kelendzheridze, “To the theory of optimal pursuit,” DAN SSSR, 138, No. 3, 151-155 (1961).

    Google Scholar 

  46. N. N. Krasovskii and A. I. Subbotin, Positional Differential Games [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  47. B. N. Pshenichnyi and V. V. Ostapenko, Differential Games [in Russian], Naukova Dumka, Kiev (1992).

    Google Scholar 

  48. B. N. Pshenichnyi, “Linear differential games,” Avtom. Telemekh., No. 1, 65-78 (1968).

  49. B. N. Pschenitchny, “e-strategies in differential games,” in: Topics in Differential Games, North Holland, New York-London-Amsterdam (1973), pp. 45-99.

    Google Scholar 

  50. A. A. Chikrii, “Differential games with several pursuers,” in: Tr. Banach Intern. Math. Center, Warsaw. Math. Control Theory, 14, 81-107 (1985).

    Google Scholar 

  51. B. N. Pshenichnyi and Yu. N. Onopchuk, “Linear differential games with integral constraints,” Tekh. Kibern., No. 1, 13-22 (1968).

  52. B. N. Pshenichnyi, A. A. Chikrii, and I. S. Rappoport, “Group pursuit in differential games,” in: J. Leipzig Techn. High School, No. 1, 13-27 (1982).

  53. G. Ts. Dzyubenko, “Linear differential games with information lag,” Kibernetika, No. 6, 81-87 (1973).

  54. B. N. Pshenichnyi and M. I. Sagaidak, “On differential games with fixed time,” Kibernetika, No. 2, 75-81 (1970).

  55. M. Z. Zgurovskii and V. S. Mel'nik, The Nonlinear Analysis and Control of Infinite-Dimensional Systems [in Russian], Naukova Dumka, Kiev (1999).

    Google Scholar 

  56. V. V. Ostapenko and I. P. Grabovoi, “Linear differential games in a Banach space,” Kibern. Sist. Anal., No. 5, 103-110 (1997).

  57. V. V. Ostapenko, “The problem of evasion from encounter,” Avtom. Telemekh., No. 4, 16-23 (1980).

  58. B. N. Pshenichnyi and G. Ts. Dzyubenko, “A differential game with two terminal sets,” in: Mat. Metody Issled. Optimiz. Sistem, IK AN USSR, Kiev (1970), pp. 3-11.

    Google Scholar 

  59. B. N. Pshenichnyi and A. A. Chikrii, “The problem of evasion from encounter in differential games,” ZhVM MF, No. 6, 1416-1428 (1974).

  60. P. B. Gusyatnikov, The Differential-Game Theory [in Russian], MFTI, Moscow (1982).

    Google Scholar 

  61. B. N. Pshenichnyi and A. A. Chikrii, “The differential game of evasion,” Izv. AN SSSR, Tekh. Kibern., No. 1, 3-10 (1977).

  62. A. A. Chikrii, “ The Problem of avoidance for controlled dynamic objects,” J. Math., Game Theory, and Algebra, 7, No. 2/3, 81-94 (1998).

    Google Scholar 

  63. M. S. Nikol'skii, The First Pontryagin Direct Method in Differential Games [in Russian], Izd. MGU, Moscow (1984).

    Google Scholar 

  64. N. L. Grigorenko, Mathematical Methods of Control of Several Dynamic Processes [in Russian], Izd. MGU, Moscow (1990).

    Google Scholar 

  65. A. A. Chikrii, Conflict Controlled Processes, Kluwer Acad. Publ., Boston-London-Dordrecht (1997).

    Google Scholar 

  66. A. A. Chikrii and S. D. Eidel'man, “Generalized Mittag–Leffler matrix functions in game problems for evolutionary equations of fractional order,” Kibern. Sist. Anal., No. 3, 3-32 (2000).

  67. A. A. Chikrii and S. D. Eidel'man, “Control game problems for quasilinear systems with Riemann–Liouvilles fractional derivatives,” Kibern. Sist. Anal., No. 6, 66-99 (2001).

    Google Scholar 

  68. A. A. Chikrii, “Quasilinear controlled processes under conflict, dynamical systems. 2,” J. Math. Sci., 80, No. 1, 1489-1518 (1996).

    Google Scholar 

  69. A. A. Chikrii and K. G. Dzyubenko, “Bilinear Markovian processes of search for moving objects,” Probl. Upravl. Inform., No. 1, 92-107 (1997).

  70. B. N. Pshenichnyi and V. G. Pokotilo, “An observation problem for a linear plant,” PMM, 46, No. 2, 48-53 (1982).

    Google Scholar 

  71. B. N. Pshenichnyi and Yu. M. Danilin, Numerical Methods in Extremum Problems [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  72. B. N. Pshenichnyi, The Linearization Method [in Russian], Nauka, Moscow (1983).

    Google Scholar 

  73. V. M. Panin, B. N. Pshenichnyi, and T. V. Lavrina, “The methods of approximating programming under conditions of optimization,” Zh. Vych. Prikl. Mat., 89, No. 2, 137-145 (2000).

    Google Scholar 

  74. B.N. Pshenichnyi, V. M. Panin, and L. A. Sobolenko, “The linearization method in constrained optimization,” in: K.–H. Elsner (ed.), Modern Math. Methods Opt., Berlin (1993), pp. 23-42.

  75. B. N. Pshenichnyi and L. A. Sobolenko, “Inverse convex programming and parallelepiped packing,” Kibern. Sist,. Anal., No. 3, 16-26 (1996).

  76. B. N. Pshenichnyi and A. P. Yakovleva, “On the necessary extremum conditions for systems with an aftereffect,” Kibernetika, No. 3, 81-85 (1976).

  77. B. N. Pshenichnyi, Yu. N. Onopchuk, and K. B. Polinkevich, “Simulation of one class of nonlinear self-organizing systems,” DAN USSR, Ser. A, No. 4, 39-43 (1986).

  78. A. B. Kurzhanskij, B. N. Pshenichnyi, and V. G. Pokotilo, Optimal Imputs for Guaranteed Identification, A-2361, IIASA, Laxenburg (1989).

    Google Scholar 

  79. V. G. Pokotilo, “On an adaptive control of observations,” PMM, 57, Issue 1, 180-183 (1993).

    Google Scholar 

  80. V. G. Pokotilo, “Optimal experimental designs in minimax estimation problems. I—III,” Kibern. Sist. Anal., No. 6, 56-64 (1992); No. 1, 61-67 (1993); No. 4, 54-62 (1993).

  81. F. L. Chernous'ko and A. A. Melikyan, Game Problems of Control and Search [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  82. A. I. Subbotin and A. G. Chentsov, Guarantee Optimization in Control Problems [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  83. V. F. Dem'yanov and L. V. Vasil'ev, Nondifferentiable Optimization [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  84. E. A. Nurminskii, Numerical Methods of Solving Determinate and Stochastic Minimax Problems [in Russian], Naukova Dumka, Kiev (1979).

    Google Scholar 

  85. Yu. M. Ermoliev and R. Wets (eds.), Numerical Methods of Stochastic Optimization, Springer–Verlag, Berlin (1987).

    Google Scholar 

  86. N. G. Loziichuk and Yu. N. Onopchuk, “Mathematical models of the thermoregulation system of the organism and their analysis,” Kibern. Sist. Anal., No. 4, 144-158 (1995).

  87. N. Z. Shor, Nondifferentiable Optimization and Polynomial Problems, Kluwer Acad. Publ., Dordrecht (1998).

    Google Scholar 

  88. A. B. Kurzhanskii, Control and Observation under Indeterminacy Conditions [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  89. B. N. Bublik, N. F. Kirichenko, and A. B. Nakonechnyi, Minimax Estimates and Controllers in Dynamic Systems," Inst. of Cybernetics, Kiev (1978).

    Google Scholar 

  90. V. M. Kuntsevich and M. M. Lychak, Synthesis of Optimal and Adaptive Control Systems. The Game Approach [in Russian], Naukova Dumka, Kiev (1985).

    Google Scholar 

  91. G. T. Chikrii, “On search for a fixed aim by a moving object,” PMM, 48, No 4, 580-584 (1984).

    Google Scholar 

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  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kiev, Ukraine

    I. V. Sergienko & A. A. Chikrii

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  1. I. V. Sergienko
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Sergienko, I.V., Chikrii, A.A. The Scientific Heritage of B. N. Pshenichnyi. Cybernetics and Systems Analysis 38, 153–174 (2002). https://doi.org/10.1023/A:1016309910620

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