×

zbMATH — the first resource for mathematics

Sufficient conditions for the generalized problem of Bolza. (English) Zbl 0513.49010

MSC:
49K15 Optimality conditions for problems involving ordinary differential equations
49L99 Hamilton-Jacobi theories
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Frank H. Clarke, Generalized gradients and applications, Trans. Amer. Math. Soc. 205 (1975), 247 – 262. · Zbl 0307.26012
[2] Frank H. Clarke, Admissible relaxation in variational and control problems, J. Math. Anal. Appl. 51 (1975), no. 3, 557 – 576. · Zbl 0326.49031 · doi:10.1016/0022-247X(75)90107-9 · doi.org
[3] -, L’Hamiltonien en optimisation, Mimeo, Univ. British Columbia, Vancouver, B.C., 1975.
[4] Frank H. Clarke, Necessary conditions for a general control problem, Calculus of variations and control theory (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1975; dedicated to Laurence Chisholm Young on the occasion of his 70th birthday), Publ. Math. Res. Center Univ. Wisconsin, No. 36, Academic Press, New York, 1976, pp. 257 – 278.
[5] Frank H. Clarke, The generalized problem of Bolza, SIAM J. Control Optimization 14 (1976), no. 4, 682 – 699. · Zbl 0333.49023 · doi:10.1137/0314044 · doi.org
[6] Frank H. Clarke, Generalized gradients of Lipschitz functionals, Adv. in Math. 40 (1981), no. 1, 52 – 67. · Zbl 0463.49017 · doi:10.1016/0001-8708(81)90032-3 · doi.org
[7] Frank H. Clarke, Extremal arcs and extended Hamiltonian systems, Trans. Amer. Math. Soc. 231 (1977), no. 2, 349 – 367. · Zbl 0369.49011
[8] I. M. Gelfand and S. V. Fomin, Calculus of variations, Revised English edition translated and edited by Richard A. Silverman, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. · Zbl 0127.05402
[9] Philip Hartman, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. · Zbl 0123.21502
[10] Magnus R. Hestenes, Calculus of variations and optimal control theory, John Wiley & Sons, Inc., New York-London-Sydney, 1966. · Zbl 0173.35703
[11] D. Q. Mayne, Sufficient conditions for a control to be a strong minimum, J. Optimization Theory Appl. 21 (1977), no. 3, 339 – 351. · Zbl 0332.49019 · doi:10.1007/BF00933535 · doi.org
[12] D. C. Offin, A Hamilton-Jacobi approach to the differential inclusion problem, Thesis, Univ. British Columbia, Vancouver, B.C., 1979.
[13] Stephen M. Robinson, Generalized equations and their solutions. II. Applications to nonlinear programming, Math. Programming Stud. 19 (1982), 200 – 221. Optimality and stability in mathematical programming. · Zbl 0495.90077
[14] R. T. Rockafellar, Convex analysis, Princeton Univ. Press, Princeton, N.J., 1970. · Zbl 0193.18401
[15] R. T. Rockafellar, Conjugate convex functions in optimal control and the calculus of variations, J. Math. Anal. Appl. 32 (1970), 174 – 222. · Zbl 0218.49004 · doi:10.1016/0022-247X(70)90324-0 · doi.org
[16] R. Tyrrell Rockafellar, Generalized Hamiltonian equations for convex problems of Lagrange, Pacific J. Math. 33 (1970), 411 – 427. · Zbl 0199.43002
[17] R. Tyrrell Rockafellar, Optimal arcs and the minimum value function in problems of Lagrange, Trans. Amer. Math. Soc. 180 (1973), 53 – 83. · Zbl 0281.49005
[18] R. Tyrrell Rockafellar, Existence theorems for general control problems of Bolza and Lagrange, Advances in Math. 15 (1975), 312 – 333. · Zbl 0319.49001 · doi:10.1016/0001-8708(75)90140-1 · doi.org
[19] Atle Seierstad and Knut Sydsaeter, Sufficient conditions in optimal control theory, Internat. Econom. Rev. 18 (1977), no. 2, 367 – 391. · Zbl 0392.49010 · doi:10.2307/2525753 · doi.org
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.