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Jacobi-type conditions for the problem of Bolza with inequalities

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Literature cited

  1. G. A. Bliss, Lectures on the Calculus of Variations, Univ. Chicago Press (1946).

  2. E. S. Levitin, A. A. Milyutin, and N. P. Osmolovskii, “Higher-order conditions for local minimum in problems with constraints,” Usp. Mat. Nauk,33, No. 6, 85–148 (1978).

    Google Scholar 

  3. A. V. Dmitruk, “Quadratic weak minimum conditions for special regimes in optimal control problems,” Dokl. Akad. Nauk SSSR,233, No. 4, 523–526 (1977); Proc. VIII Winter School in Mathematical Programming and Related Questions, TsEMI (1976), pp. 102–119.

    Google Scholar 

  4. A. V. Dmitruk, “On the Euler-Jacobi equation in the calculus of variations,” Mat. Zametki,20, No. 6, 847–858 (1976).

    Google Scholar 

  5. K. Hazard, “Index theorems for the problem of Bolza in calculus of variations,” in: Contributions to the Calculus of Variations, 1938–1941, Univ. of Chicago Press (1942), pp. 293–356.

  6. M. R. Hestenes, “Applications of the theory of quadratic forms in Hilbert space to the calculus of variations,” Pac. J. Math.,1, No. 4, 525–581 (1951).

    Google Scholar 

  7. A. V. Dmitruk, “Jacobi-type conditions for the nonnegativity of a quadratic form on a finite-faced cone,” Izv. Akad. Nauk SSSR, Ser. Mat.,45, No. 3, 608–619 (1981).

    Google Scholar 

  8. E. G. Gol'shtein (Gol'stein), Theory of Convex Programming, Am. Math. Soc., Providence (1972).

    Google Scholar 

  9. A. A. Milyutin, “On quadratic extremum conditions in smooth problems with a finitedimensional image,” in: Methods of the Theory of Extremal Problems in Economics [in Russian], Nauka, Moscow (1981), pp. 138–177.

    Google Scholar 

  10. A. Ya. Dubovitskii and A. A. Milyutin, “Extremal problems in the presence of constraints,” Zh. Vychisl. Mat. Mat. Fiz.,5, No. 3, 395–453 (1965).

    Google Scholar 

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    A. V. Dmitruk

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  1. A. V. Dmitruk
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Translated from Matematicheskie Zametki, Vol. 35, No. 6, pp. 813–827, June, 1984.

The author expresses his gratitude to A. A. Milyutin for his constant interest and help and also to N. P. Osmolovskii for useful discussions.

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Dmitruk, A.V. Jacobi-type conditions for the problem of Bolza with inequalities. Mathematical Notes of the Academy of Sciences of the USSR 35, 427–435 (1984). https://doi.org/10.1007/BF01139945

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