Literature Cited
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).
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).
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).
V. S. Mikhalevich, N. N. Redkovskii, and A. E. Perekatov, “Methods of minimization of functions on simple sets,” Kibernetika, No. 4, 25–35 (1986).
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).
D. C. Sorensen, “Newton's method with a model trust region modification,” SIAM J. Numer. Anal.,19, No. 2, 409–426 (1982).
J. J. More and D. C. Sorensen, “Newton's method,” Report Argonne Nat. Lab. ANL-82-8, Argonne (1982).
J. J. More and D. C. Sorensen, “Computing a trust region step,” SIAM J. Sci. Stat. Comput.,4, No. 3, 553–572 (1983).
W. Murray, “Failure: the causes and cures,” in: Numerical Methods for Unconstrained Optimization, W. Murray (ed.), Academic Press, NY (1972).
F. S. Sisser, “Elimination of bounds in optimization problems by transforming variables,” Math. Program.,20, 110–121 (1981).
F. Gill, W. Murray, and M. Wright, Practical Optimization [Russian translation], Mir, Moscow (1985).
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).
B. N. Pshenichnyi and N. N. Redkovskii, “Some methods of unconstrained minimization,” Zh. Vychisl. Mat. Mat. Fiz.,19, No. 5, 1127–1133 (1979).
V. V. Voevodin, Computational Foundations of Linear Algebra [in Russian], Nauka, Moscow (1977).
N. N. Redkovskii, “Using curvilinear coordinates for minimization of nonconvex functions,” Kibernetika, No. 2, 117–118 (1982).
N. N. Redkovskii, “On one method of minimization of smooth nonconvex functions,” Ekono. Mat. Metody, No. 5, 906–911 (1983).
N. N. Redkovskii, “Using nonlinear transformations in unconstrained minimization problems,” Dokl. Akad. Nauk UkrSSR, No. 3, 69–72 (1985).
N. N. Redkovskii, “Methods of minimization with nonlinear transformation of coordinates,” Dokl. Akad. Nauk SSSR,288 No. 3, 556–560 (1986).
B. Parlett, The Symmetrical Eigenvalue Problem: Numerical Methods [Russian translation], Mir, Moscow (1983).
M. D. Hebden, “An algorithm for minimization using exact second derivatives,” TP 515, Atomic Energy Research Establishment, Harwell (1973).
D. M. Gay, “Computing an optimal locally constrained step,” SIAM J. Sci. Stat. Comput.,2, 186–197 (1981).
C. H. Reinch, “Smoothing by spline functions. II,” Numer. Math.,16, No. 5, 451–454 (1971).
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).
F. P. Vasil'ev Methods of Solution of Extremal Problems [in Russian], Nauka, Moscow (1981).
L. Elden, “Algorithms for regularization of ill-conditioned least squares problems,” BIT,17, No. 2, 134–145 (1977).
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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