Dual variational methods in non-convex optimization and differential equations

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Part of the Lecture Notes in Mathematics book series (LNM, volume 979)


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  1. 1.
    AUBIN-EKELAND, "Second-order evolution equations with convex Hamiltonian", Canadian Math. Bull. 23 (1980) p. 81–94.CrossRefzbMATHGoogle Scholar
  2. 2.
    AUCHMUTY, "Duality for non-convex variational principles", preprint, Indiana University, Bloomington, 1981.zbMATHGoogle Scholar
  3. 3.
    BREZIS-CORON-NIRENBERG, "Free vibrations for a nonlinear wave equation and a theorem of P. Rabinowitz", Comm. Pure App. Math. 33 (1980), p.667–684.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    CLARKE, "Solution périodique des équations hamiltoniennes", CRAS Paris, 287, 1978, p.951–2.zbMATHGoogle Scholar
  5. 5.
    CLARKE, "Periodic solutions to Hamiltonian inclusions", J. Diff. Eq. 40, 1981, p.1–6.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    CLARKE, "On Hamiltonian flows and symplectic transformations", SIAM J. Control and Optimization, in press.Google Scholar
  7. 7.
    CLARKE-EKELAND, "Solutions periodiques, de periode donnée, des équations hamiltoniennes", CRAS Paris 287, 1978, p.1013–1015.zbMATHGoogle Scholar
  8. 8.
    CLARKE-EKELAND, "Hamiltonian trajectories having prescribed minimal period", Comm. Pure App. Math., 33 (1980), p.103–116.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    CLARKE-EKELAND, "Nonlinear oscillations and boundary-value problems for Hamiltonian systems", Archive Rat. Mech. An., in press.Google Scholar
  10. 10.
    EKELAND, "Duality in non-convex optimization and calculus of variations", SIAM J. Opt. Con. 15, 1977, p.905–934.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    EKELAND, "Periodic solutions to Hamiltonian equations and a theorem of P. Rabinowitz", J. Diff. Eq. 34, 1979, p.523–534.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    EKELAND, "Forced oscillations for nonlinear Hamiltonian systems II", Advances in Mathematics, volume in honor of Laurent Schwartz, Nachbin ed., 1981, Academic Press.Google Scholar
  13. 13.
    EKELAND, "Oscillations forcées de systémes hamiltoniens non linéaires III", Bulletin de la SMF, in press.Google Scholar
  14. 14.
    EKELAND, "Dualité et stabili té des systémes hamiltoniens", preprint 1981.Google Scholar
  15. 15.
    EKELAND, "A perturbation theory near convex Hamiltonian systems", preprint, 1981.Google Scholar
  16. 16.
    EKELAND-LASRY, "Principes variationnels en dualité", CRAS Paris, 291 (1980), p.493–497.zbMATHGoogle Scholar
  17. 17.
    EKELAND-LASRY, "Duality in nonconvex variational problems", preprint, CEREMADE, 1980.Google Scholar
  18. 18.
    EKELAND-LASRY, "On the number of closed trajectories for a Hamiltonian system on a convex energy surface", Annals of Math., 112 (1980), p.283–319.CrossRefzbMATHGoogle Scholar
  19. 19.
    EKELAND-TEMAM, "Convex analysis and variational problems", North-Holland-Elsevier, 1976.Google Scholar
  20. 20.
    TOLAND, "Stability of heavy rotating chains", J. Diff. Eq. 32 (1979), p.15–31.MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    TOLAND, "A duality principle for non-convex optimization and the calculus of variations", Arch. Rat. Mech. An. 71 (1979), p. 41–61.MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    TOLAND, "Duality in nonconvex optimization", J. Math. An. Appl. 66 (1978), p.41–61.MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    TRUC, Thése 3eme cycle, en cours, Université Paris-Dauphine.Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  1. 1.Department of Mathematics, U.B.C.France
  2. 2.CEREMADE, Université Paris-DauphineFrance

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