Sufficient conditions in the calculus of variations and in the theory of optimal control
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- by Zeev Nehari
- Proc. Amer. Math. Soc. 39 (1973), 535-539
- DOI: https://doi.org/10.1090/S0002-9939-1973-0319007-1
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Abstract:
A method is described for obtaining criteria confirming the optimality of solutions found either by integrating the Euler-Lagrange equations, or by applying the Pontrjagin necessary condition. The method is based on convexity considerations, and its success in a given problem depends on the judicious choice of certain arbitrary auxiliary functions.References
- C. Carathéodory, Variationsrechnung und partielle Differentialgleichungen erster Ordnung, Teubner, Leipzig, 1935.
- J. E. Funk and E. G. Gilbert, Some sufficient conditions for optimality in control problems with state space constraints, SIAM J. Control 8 (1970), 498–504. MR 0295801
- Morton I. Kamien and Nancy L. Schwartz, Sufficient conditions in optimal control theory, J. Econom. Theory 3 (1971), 207–214. MR 448208, DOI 10.1016/0022-0531(71)90018-4
- O. L. Mangasarian, Sufficient conditions for the optimal control of nonlinear systems, SIAM J. Control 4 (1966), 139–152. MR 0189864
- L. S. Pontrjagin, V. G. Boltjanskiĭ, R. V. Gamkrelidze, and E. F. Miščenko, Matematicheskaya teoriya optimal′nykh protsessov, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1961 (Russian). MR 0166036
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 39 (1973), 535-539
- MSC: Primary 49B10
- DOI: https://doi.org/10.1090/S0002-9939-1973-0319007-1
- MathSciNet review: 0319007