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Mat. Sb., 2004, Volume 195, Number 6, Pages 57–70 (Mi msb826)  

This article is cited in 4 scientific papers (total in 4 papers)

Hessian of the solution of the Hamilton–Jacobi equation in the theory of extremal problems

M. I. Zelikin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: An optimal control problem with separated conditions at the end-points is studied. It is assumed that there exists on the manifold of left end-points (as well as on the manifold of right end-points) a field of extremals containing the fixed extremal. A criterion describing necessary and sufficient conditions of optimality in terms of these two fields is proved. The sufficient condition is the positive-definiteness of the difference of the solutions of the corresponding matrix Riccati's equations and the necessary one is its non-negativity. The key part in the proof of the criterion is played by a formula relating the solution of Riccati's equation and the Hessian of the Bellman function.

DOI: https://doi.org/10.4213/sm826

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English version:
Sbornik: Mathematics, 2004, 195:6, 819–831

Bibliographic databases:

UDC: 517.977
MSC: Primary 49K15, 93C15; Secondary 49L20
Received: 24.12.2003

Citation: M. I. Zelikin, “Hessian of the solution of the Hamilton–Jacobi equation in the theory of extremal problems”, Mat. Sb., 195:6 (2004), 57–70; Sb. Math., 195:6 (2004), 819–831

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Zelikin M.I., “On Multiple Integral Minimization Problems”, XXIX Workshop on Geometric Methods in Physics, AIP Conference Proceedings, 1307, 2010, 209–218  crossref  mathscinet  zmath  adsnasa  isi
    2. S. Bellucci, B.N. Tiwari, “Thermodynamic geometry: Evolution, correlation and phase transition”, Physica A: Statistical Mechanics and its Applications, 390:11 (2011), 2074  crossref  mathscinet  adsnasa  isi
    3. M. I. Zelikin, “Theory of fields of extremals for multiple integrals”, Russian Math. Surveys, 66:4 (2011), 733–765  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. M. I. Zelikin, “Field theories for multiple integrals”, J Math Sci, 177:2 (2011), 270–298  crossref  mathscinet  zmath
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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