Journal of Mathematical Sciences

, Volume 188, Issue 3, pp 299–321 | Cite as

Numerical methods in problems of calculus of variations for functionals depending on higher order derivatives

  • G. Sh. Tamasyan

Nonsmooth analysis and the exact penalization theory are used for studying variational problems with functionals depending on higher order derivatives. We obtain the extremum conditions and develop “direct” minimization methods, in particular, the steepest descent method and the hypodifferential descent method. Bibliography: 8 titles.


Local Minimizer Stationary Point Steep Descent Descent Method Classical Variation 
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  1. 1.
    V. F. Demyanov, Extremality Conditions and Variational Problems [in Russian], Vyssh. Shkola, Moscow (2005).Google Scholar
  2. 2.
    I. I. Eremin, “The “penalty” method in convex programming” [in Russian], Dokl. Akad. Nauk SSSR 173, 748–751 (1967); English transl.: Sov. Math., Dokl. 8, 459–462 (1967).MATHGoogle Scholar
  3. 3.
    V. F. Demyanov and G. Sh. Tamasyan, “Exact penalty functions in isoperimetric problems,” Optimization 60, No. 1–3, 153–177 (2011).MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    V. F. Demyanov, “Exact penalty functions in problems of nonsmooth optimization” [in Russian], Vestn. St-Peterbg. Univ., Ser. I No. 4, 21–27 (1994); English transl.: Vestn. St. Petersbg. Univ., Math. 27, No. 4, 16-22 (1994).MathSciNetMATHGoogle Scholar
  5. 5.
    V. F. Demyanov and A. M. Rubinov, Constructive Nonsmooth Analysis [in Russian], Nauka, Moscow (1990); English transl.: Verlag Peter Lang, Frankfurt/Main (1995).Google Scholar
  6. 6.
    F. R. Gantmakher, Theory of Matrices [in Russian], Fizmatlit, Moscow (1988).Google Scholar
  7. 7.
    N. M. Gunter, Lectures on Calculus of Variations [in Russian], Gostehizdat, Moscow (1941).Google Scholar
  8. 8.
    A. Yu. Uteshev and G. Sh. Tamasyan, “On the polynomial interpolation problem with multiple knots” [in Russian], Vest. St.-Peterburg Univ., Ser 10: Prikl. Mat. Inform. No. 3, 76-85 (2010).Google Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Sankt-Petersburg State UniversitySt.-PetersburgRussia

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