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
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.
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Sbornik: Mathematics, 2004, 195:6, 819–831
MSC: Primary 49K15, 93C15; Secondary 49L20
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
\paper Hessian of the solution of the Hamilton--Jacobi equation in the theory of~extremal problems
\jour Mat. Sb.
\jour Sb. Math.
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Zelikin M.I., “On Multiple Integral Minimization Problems”, XXIX Workshop on Geometric Methods in Physics, AIP Conference Proceedings, 1307, 2010, 209–218
S. Bellucci, B.N. Tiwari, “Thermodynamic geometry: Evolution, correlation and phase transition”, Physica A: Statistical Mechanics and its Applications, 390:11 (2011), 2074
M. I. Zelikin, “Theory of fields of extremals for multiple integrals”, Russian Math. Surveys, 66:4 (2011), 733–765
M. I. Zelikin, “Field theories for multiple integrals”, J Math Sci, 177:2 (2011), 270–298
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