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Nonlinear structure methods in optimization problems: A survey of the work of N. N.Redkovskii

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References

  1. B. N. Pshenichnyi and N. N. Redkovskii, “A numerical minimization method without derivatives,” Zh. Vychisl. Matern, i Mat. Fiziki,16, No. 6, 1388–1396 (1976).

    Google Scholar 

  2. N. N. Redkovskii, “Using the conjugate direction method for derivative-free minimization,” in: Optimal Decision Theory [in Russian], Inst. Kibern. Akad. Nauk UkrSSR, Kiev (1976), pp. 28–39.

    Google Scholar 

  3. N. N. Redkovskii, “A derivative-free minimization algorithm for problems in production control systems,” in: Mechanization and Automation in Management [in Russian], No. 4, UkrNIINTI, Kiev (1976), pp. 14–16.

    Google Scholar 

  4. N. N. Redkovskii, A Derivative-Free Minimization Algorithm for Convex Functions [in Russian], Inst. Kibern. Akad. Nauk UkrSSR, Kiev (1976). Unpublished manuscript, GosFAP SSSR No. 186.

    Google Scholar 

  5. B. N. Pshenichnyi and N. N. Redkovskii, “A method for minimization along eigenvectors of a matrix close to the Hessian,” Kibernetika, No. 6, 68–74 (1977).

  6. N. N. Redkovskii, “A derivative-free minimization algorithm for functions of many variables,” in: Optimal Decision Theory [in Russian], Inst. Kibern. Akad. Nauk UkrSSR, Kiev (1977), pp. 55–59.

    Google Scholar 

  7. N. N. Redkovskii, Development of Derivative-Free Numerical Minimization Methods [in Russian], abstract of candidate thesis, Kiev (1977).

  8. B. N. Pshenichnyi and N. N. Redkovskii, “Some methods of unconstrained minimization,” Zh. Vychisl. Matern, i Mat. Fiziki,19, No. 5, 1127–1133 (1979).

    Google Scholar 

  9. A. A. Antonyuk, A. P. Bulanyi, Yu. M. Danilin, and N. N. Redkovskii, Application Software for Unconstrained Minimization Problems [in Russian], Inst. Kibern. Akad. Nauk UkrSSR, Kiev (1980). Unpublished manuscript, GosFAP SSSR No. 5893.

    Google Scholar 

  10. A. A. Antonyuk, A. P. Bulanyi, Yu. M. Danilin, and N. N. Redkovskii, “A software package for unconstrained minimization problems,” USiM, No. 4, 3–4 (1981).

  11. A. M. Antonov, N. N. Redkovskii, and L. A. Prokopenko, “Application of an unconstrained optimization method to solve an inverse boundary-value problem with a free boundary,” Vychisl. i Prikl. Matem., Kiev, No. 47, 90–97 (1981).

  12. N. N. Redkovskii, “Solving minimization problems with equality constraints in one special case,” in: Methods of Investigation of Extremal Problems [in Russian], Inst. Kibern. Akad. Nauk UkrSSR, Kiev (1981), pp. 87–92.

    Google Scholar 

  13. N. N. Redkovskii, Curvilinear Descent Methods in Unconstrained Minimization [in Russian], Preprint No. 81-55, Inst. Kibern. Akad. Nauk UkrSSR, Kiev (1981).

    Google Scholar 

  14. N. N. Redkovskii, “Construction of algorithms for systems of nonlinear equations,” Dokl. Akad. Nauk UkrSSR, No. 5, 74–77 (1982).

  15. N. N. Redkovskii, “Numerical method for solving systems of nonlinear equations,” Dokl. Akad. Nauk SSSR, 262, No. 5, 1319–1321 (1982).

  16. N. N. Redkovskii, “Unconstrained minimization methods based on a nonconvex function model,” Dokl. Akad. Nauk UkrSSR, No. 3, 64–67 (1982).

  17. N. N. Redkovskii, “Some minimization methods for solving problems with equality constraints,” Zh. Vychisl. Matem. Mat. Fiziki,22, No. 1, 36–42 (1982).

    Google Scholar 

  18. N. N. Redkovskii, “Using curvilinear coordinates for minimization of nonconvex functions,” Kibernetika, No. 2, 117–118 (1982).

  19. N. N. Redkovskii and A. E. Perekatov, “An optimization method for control problems in continuous technological processes,” in: Experience with Design and Creation of General-System Support Tools for Intersectoral MIS [in Russian], Glavnivts Gosplana UkrSSR, Kiev (1982), pp. 154–156.

    Google Scholar 

  20. N. N. Redkovskii and A. E. Perekatov, “Curvilinear descent method for minimization with linear constraints,” in: Mathematical Methods of Analysis of Extremal Problems [in Russian], Inst. Kibern. Akad. Nauk UkrSSR, Kiev (1983), pp. 15–19.

    Google Scholar 

  21. N. N. Redkovskii, “Numerical method for solving systems of nonlinear equations by curvilinear descent,” Zh. Vychisl. Matem. i Mat. Fiziki,23, No. 2, 261–266 (1983).

    Google Scholar 

  22. N. N. Redkovskii, “A minimization method using curvilinear descent,” Kibernetika, No. 5, 93–95 (1983).

  23. N. N. Redkovskii, “Rate of convergence of the Powell method,” Kibernetika, No. 2, 115–117 (1983).

  24. N. N. Redkovskii and A. E. Perekatov, “Numerical method to find the minimum of functions on a sphere,” Dokl. Akad. Nauk UkrSSR, No. 9, 71–73 (1983).

  25. N. N. Redkovskii, “A minimization method for smooth nonconvex functions,” Ekon. i Mat. Metody, No. 5, 906–911 (1983).

  26. V. S. Mikhalevich and N. N. Redkovskii, “Successive method for minimization of a nonlinear function on a simplex,” Dokl. Akad. Nauk SSSR,274, No. 3, 544–547 (1983).

    Google Scholar 

  27. N. N. Redkovskii, “Computation of a parametric surface where a function attains an extremum,” Dokl. Akad. Nauk UkrSSR, No. 3, 73–75 (1984).

    Google Scholar 

  28. N. N. Redkovskii and Yu. A. Mikhailin, “A minimization method using a curvilinear descent scheme,” in: Methods of Solving Nonlinear and Discrete Programming Problems [in Russian], Inst. Kibern. Akad. Nauk UkrSSR, Kiev (1984), pp. 84–85.

    Google Scholar 

  29. B. N. Pshenichnyi, A. A. Chikrii, N. N. Redkovskii, E. V. Klimenko, and A. E. Perekatov, Discrete Search Problem [in Russian], Preprint 84-12, Inst. Kibern. Akad. Nauk UkrSSR, Kiev (1984).

    Google Scholar 

  30. V. S. Mikhalevich, N. N. Redkovskii, and A. E. Perekatov, “Numerical minimization methods for nonlinear functions on nonintersecting simplexes,” Kibernetika, No. 1, 1–10 (1985).

  31. N. N. Redkovskii, “Using nonlinear transformations in unconstrained minimization problems,” Dokl. Akad. Nauk UkrSSR, No. 3, 69–72 (1985).

  32. N. N. Redkovskii, “A solution of a nonlinear programming problem with equality constraints,” Kibernetika, No. 4, 47–51 (1985).

  33. V. S. Mikhalevich and N. N. Redkovskii, “Finding the minimum on the set of symmetric nonnegative definite matrices,” Dokl. Akad. Nauk SSSR,283, No. 5, 1081–1085 (1985).

    Google Scholar 

  34. N. N. Redkovskii and A. E. Perekatov, “Minimization of functions on a parallelepiped,” Dokl. Akad. Nauk UkrSSR, No. 11, 60–64 (1985).

  35. N. N. Redkovskii, “Restricting the set of limit points of a minimization algorithm,” Kibernetika, No. 6, 124–125 (1985).

  36. N. N. Redkovskii, “Minimization method with nonlinear transformation of coordinates,” Dokl. Akad. Nauk SSSR,288, No. 3, 556–560 (1986).

    Google Scholar 

  37. V. S. Mikhalevich, N. N. Redkovskii, and A. E. Perekatov, “Minimization methods for functions on simple sets,” Kibernetika, No. 4, 25–35 (1986).

  38. V. S. Mikhalevich and N. N. Redkovskii, “Numerical minimization method on the set of positive definite matrices,” Dokl. Akad. Nauk SSSR,290, No. 4, 809–812 (1986).

    Google Scholar 

  39. V. S. Mikhalevich, N. N. Redkovskii, and A. A. Antonyuk, “Some minimization methods on the set of nonnegative definite matrices,” Kibernetika, No. 6, 84–90 (1986).

  40. A. A. Antonyuk and N. N. Redkovskii, A Program for Computing the Matrix of Diffusion Coefficients of Two-Component Mixtures in Porous Media [in Russian], Inst. Kibern. Akad. Nauk UkrSSR, Kiev (1986). Unpublished manuscript, GosFAP SSSR No. 50870000126, 29.09.86.

    Google Scholar 

  41. A. A. Antonyuk, R. M. Marutovskii, and N. N. Redkovskii, “Numerical solution of the inverse problem of nonstationary mass transfer in multicomponent mixtures,” Inzhenerno-Fizicheskii Zh.,53, No. 1, 113–117 (1987).

    Google Scholar 

  42. A. E. Perekatov and N. N. Redkovskii, “Combined minimization method for problems with interval constraints,” Dokl. Akad. Nauk UkrSSR, No. 8, 73–76 (1987).

  43. V. S. Mikhalevich, N. N. Redkovskii, and A. E. Perekatov, “Minimization methods for functions on a sphere and their applications,” Kibernetika, No. 6, 1–8 (1987).

  44. A. E. Perekatov and N. N. Redkovskii, A Program for Minimization of Functions on a Parallelepiped [in Russian], Inst. Kibern. Akad. Nauk UkrSSR, Kiev (1987). Unpublished manuscript, GosFAP SSSR No. 50870000649.

    Google Scholar 

  45. N. N. Redkovskii, “Minimization methods with nonlinear transformation of coordinates,” in: Application of Nonlinear Programming and Optimization in Management, abstracts of papers at IFAC 7th Seminar [in Russian], Inst. Problem Upravleniya Akad. Nauk SSSR, Moscow (1988), pp. 54–55.

    Google Scholar 

  46. A. A. Antonyuk, R. M. Marutovskii, P. F. Zhuk, M. Byulov, and N. N. Redkovskii, “Direct and inverse problems of nonstationary mass transfer in multicomponent mixtures in adsorbents with catalytic properties,” Teoret. Osnovy Khim. Tekhnol.,22, No. 4, 476–480 (1988).

    Google Scholar 

  47. V. S. Mikhalevich, N. N. Redkovskii, and A. A. Antonyuk, “On minimization methods for smooth nonconvex functions,” Kibernetika, No. 4, 6–12 (1988).

  48. N. N. Redkovskii, “Models of unimodal nonconvex functions and unconstrained minimization methods,” in: Optimization Methods in Economic Modeling [in Russian], TsEMI Akad. Nauk SSSR, Moscow (1988), pp. 199–211.

    Google Scholar 

  49. N. N. Redkovskii, Nonlinear Structure Methods in Optimization Problems [in Russian], abstract of doctoral dissertation, Kiev (1988).

  50. A. E. Perekatov and N. N. Redkovskii, “Minimization method for unimodal nonconvex functions,” Dokl. Akad. Nauk UkrSSR, No. 10, 36–38 (1989).

  51. A. E. Perekatov and N. N. Redkovskii, “Mathematical modeling of thermal regeneration in adsorbents,” in: Modeling and Simulation in Design and Control Systems, abstracts of papers of All-Union Conf. [in Russian], MGTsNTI, Chernigov (1990), pp. 231–232.

    Google Scholar 

  52. V. S. Mikhalevich, N. N. Redkovskii, A. A. Antonyuk, R. M. Marutovskii, and I. G. Roda, “Minimization methods on a set of matrices and identification problems in some mass-transfer models,“ Kibernetika, No. 2, 78–83 (1990).

  53. A. A. Antonyuk, N. G. Antonyuk, R. M. Marutovskii, N. N. Redkovskii, and I. G. Roda, “Solving dynamic system identification problems: modeling of sorption processes,” Elektronnoe Modelirovanie,12, No. 4, 99–101 (1990).

    Google Scholar 

  54. N. N. Redkovskii, “A numerical method for solving systems of nonlinear equations,” Kibernetika, No. 3, 60–64 (1990).

  55. N. N. Redkovskii, A. A. Antonyuk, A. E. Perekatov, N. A. Klimenko, M. N. Timoshenko, S. V. Grechanik, and V. V. Slobodyan, “Modeling the heating stage in thermo-oxidative regeneration of activated carbon developed for waste water purification,” Khimiya i Tekhnologiya Vody, 12, No. 11, 963–967 (1990).

    Google Scholar 

  56. V. S. Mikhalevich, N. N. Redkovskii, A. A. Antonyuk, and A. E. Perekatov, “On nonconvex approximations in unconstrained minimization,” Kibernetika, No. 6, 20–29 (1990).

  57. A. A. Antonjuk, N. N. Redkovsky, P. S. Carl, A. Seidel, and R. M. Manitovsky, “Determination of intraparticle kinetic parameters for adsorption of binary solutions on activated carbon,” Chem. Eng. Sci.,46, No. 4, 1035–1039 (1991).

    Article  Google Scholar 

  58. N. N. Redkovskii, M. N. Timoshenko, N. A. Klimenko, A. A. Antonyuk, S. V. Grechanik, A. E. Perekatov, and V. V. Slobodyan, “A mathematical model of thermo-oxidative regeneration of activated carbon used for waste water purification,” Khimiya i Tekhnologiya Vody,13, No. 1, 9–11 (1991).

    Google Scholar 

  59. A. V. Gureev and N. N. Redkovskii, “A method for solving systems of equations for determination of the operating conditions of electrical networks,” Kibernetika i Sistemnyi Analiz, No. 2, 3–12 (1993).

  60. V. A. Gureev and N. N. Redkovskii, “Solving nonlinear equations in control problems for operation of electrical networks,” Kibernetika i Sistemnyi Analiz, No. 4, 122–130 (1993).

  61. V. A. Gureev and N. N. Redkovskii, “Parametric method for computing the characteristics of steady-state operation of electrical networks,” Kibernetika i Sistemnyi Analiz, No. 1, 140–146 (1994).

  62. V. A. Gureev and N. N. Redkovskii, “Numerical determination of steady-state operating conditions in electrical networks,” Elektronnoe Modelirovanie, No. 4, 59–62 (1994).

  63. V. A. Gureev and N. N. Redkovskii, “A method for simultaneous calculation of steady-state operating conditions and minimum losses in electrical networks,” Kibernetika i Sistemnyi Analiz, No. 6, 145–152 (1994).

  64. V. A. Gureev and N. N. Redkovskii, “On some features of numerical calculation of voltages for steady-state modeling of electric power systems,” Elektronnoe Modelirovanie, No. 1, 92–96 (1995).

  65. N. N. Redkovskii and V. A. Gurev, “On behavior strategies of iterative methods with a singular Jacobian,” Kibernetika i Sistemnyi Analiz, No. 2, 90–102 (1996).

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  1. N. N. Redkovskii
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  2. A. A. Antonyuk
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Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 121–130, January–February, 1997.

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Redkovskii, N.N., Antonyuk, A.A. Nonlinear structure methods in optimization problems: A survey of the work of N. N.Redkovskii. Cybern Syst Anal 33, 97–104 (1997). https://doi.org/10.1007/BF02665947

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