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Methods of minimization of functions on a sphere and their applications

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Literature Cited

  1. V. S. Mikhalevich and N. N. Redkovskii, “Sequential method of minimization of a nonlinear function on a simplex,” Dokl. Akad. Nauk SSSR,274, No. 3, 544–547 (1984).

    Google Scholar 

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

    Google Scholar 

  3. V. S. Mikhalevich and N. N. Redkovskii, “Seeking the minimum of a function on the set of symmetrical nonnegative definite matrices,” Dokl. Akad. Nauk SSSR,283, No. 5, 1081–1085 (1985).

    Google Scholar 

  4. V. S. Mikhalevich, N. N. Redkovskii, and A. E. Perekatov, “Methods of minimization of functions on simple sets,” Kibernetika, No. 4, 25–35 (1986).

    Google Scholar 

  5. N. N. Redkovskii and A. E. Perekatov, “A numerical minimum-seeking method for functions on a sphere,” Dokl. Akad. Nauk UkrSSR, No. 9, 71–73 (1983).

    Google Scholar 

  6. D. C. Sorensen, “Newton's method with a model trust region modification,” SIAM J. Numer. Anal.,19, No. 2, 409–426 (1982).

    Google Scholar 

  7. J. J. More and D. C. Sorensen, “Newton's method,” Report Argonne Nat. Lab. ANL-82-8, Argonne (1982).

  8. J. J. More and D. C. Sorensen, “Computing a trust region step,” SIAM J. Sci. Stat. Comput.,4, No. 3, 553–572 (1983).

    Google Scholar 

  9. W. Murray, “Failure: the causes and cures,” in: Numerical Methods for Unconstrained Optimization, W. Murray (ed.), Academic Press, NY (1972).

    Google Scholar 

  10. F. S. Sisser, “Elimination of bounds in optimization problems by transforming variables,” Math. Program.,20, 110–121 (1981).

    Google Scholar 

  11. F. Gill, W. Murray, and M. Wright, Practical Optimization [Russian translation], Mir, Moscow (1985).

    Google Scholar 

  12. B. N. Pshenichnyi and N. N. Redkovskii, “On a numerical method of minimization without computing the derivatives,” Zh. Vychisl. Mat. Mat. Fiz.,16, No. 6, 1388–1396 (1976).

    Google Scholar 

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

    Google Scholar 

  14. V. V. Voevodin, Computational Foundations of Linear Algebra [in Russian], Nauka, Moscow (1977).

    Google Scholar 

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

    Google Scholar 

  16. N. N. Redkovskii, “On one method of minimization of smooth nonconvex functions,” Ekono. Mat. Metody, No. 5, 906–911 (1983).

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  19. B. Parlett, The Symmetrical Eigenvalue Problem: Numerical Methods [Russian translation], Mir, Moscow (1983).

    Google Scholar 

  20. M. D. Hebden, “An algorithm for minimization using exact second derivatives,” TP 515, Atomic Energy Research Establishment, Harwell (1973).

  21. D. M. Gay, “Computing an optimal locally constrained step,” SIAM J. Sci. Stat. Comput.,2, 186–197 (1981).

    Google Scholar 

  22. C. H. Reinch, “Smoothing by spline functions. II,” Numer. Math.,16, No. 5, 451–454 (1971).

    Google Scholar 

  23. A. K. Cline, C. B. Moler, G. W. Stewart, and I. H. Wilkinson, “An estimate for the condition number of a matrix,” SIAM J. Numer. Anal.,16, No. 2, 368–375 (1979).

    Google Scholar 

  24. F. P. Vasil'ev Methods of Solution of Extremal Problems [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  25. L. Elden, “Algorithms for regularization of ill-conditioned least squares problems,” BIT,17, No. 2, 134–145 (1977).

    Google Scholar 

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Translated from Kibernetika, No. 6, pp. 1–8, November–December, 1987.

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Mikhalevich, V.S., Redkovskii, N.N. & Perekatov, A.E. Methods of minimization of functions on a sphere and their applications. Cybern Syst Anal 23, 721–730 (1987). https://doi.org/10.1007/BF01070232

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  • DOI: https://doi.org/10.1007/BF01070232

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