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Nonoccurrence of gap for infinite-dimensional control problems with nonconvex integrands

Pages 171-186 | Received 05 Nov 2004, Accepted 01 Sep 2005, Published online: 11 Oct 2011

References

  • Ahmed , NU . 2003 . Generalized solutions of HJB equations applied to stochastic control on Hilbert space. . Nonlinear Analysis. Theory Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods , 54 : 495 – 523 .
  • Ahmed , NU . 2003 . Existence of optimal controls for a general class of impulsive systems on Banach spaces. . SIAM Journal on Control and Optimization , 42 : 669 – 685 .
  • Alberti , G and Serra Cassano , F . 1994 . “ Non-occurrence of gap for one-dimensional autonomous functionals, Calculus of variations, homogenization and continuum mechanics (Marseille, 1993) ” . In Series on Advances in Mathematics for Applied Sciences , Vol. 18 , 1 – 17 . River Edge NJ : World Sci. Publishing .
  • Angell , TS . 1979 . A note on the approximation of optimal solutions of the calculus of variations. . Rendiconti del Circolo Matematico di Palermo. Serie II , 2 : 258 – 272 .
  • Ball , JM and Mizel , VJ . 1984 . Singular minimizers for regular one-dimensional problems in the calculus of variations. . American Mathematical Society. Bulletin. New Series , 11 : 143 – 146 .
  • Ball , JM and Mizel , VJ . 1985 . One-dimensional variational problems whose minimizers do not satisfy the Euler-Lagrange equation. . Archive for Rational Mechanics and Analysis , 90 : 325 – 388 .
  • Bensoussan , A , Da Prato , G , Delfour , MC and Mitter , SK . 1992 . Representation and Control of Infinite Dimensional Systems , Vol. I and II , Boston : Birkhauser .
  • Brezis , H . 1973 . Opérateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert Amsterdam, , North Holland
  • Carlson , DA , Haurie , A and Leizarowitz , A . 1991 . Infinite Horizon Optimal Control , Berlin : Springer-Verlag .
  • Cesari , L . 1983 . Optimization-theory and Applications , Berlin : Springer-Verlag .
  • Clarke , FH and Vinter , RB . 1985 . Regularity properties of solutions to the basic problem in the calculus of variations. . Transactions of the American Mathematical Society , 289 : 73 – 98 .
  • Clarke , FH and Vinter , RB . 1986 . Regularity of solutions to variational problems with polynomial Lagrangians. . Bulletin of the Polish Academy of Sciences , 34 : 73 – 81 .
  • Lavrentiev , M . 1926 . Sur quelques problemes du calcul des variations . Annali di Matematica Pura ed Applicata , 4 : 107 – 124 .
  • Loewen , PD . 1987 . On the Lavrentiev phenomenon. . Canadian Mathematical Bulletin. Bulletin Canadien de Mathematiques , 30 : 102 – 108 .
  • Mania , B . 1934 . Sopra un esempio di Lavrentieff. . Boll. Un. Mat. Ital. , 13 : 146 – 153 .
  • Sychev , MA and Mizel , VJ . 1998 . A condition on the value function both necessary and sufficient for full regularity of minimizers of one-dimensional variational problems. . Transactions of the American Mathematical Society , 350 : 119 – 133 .
  • Zaslavski , AJ . 2005 . Nonoccurrence of the Lavrentiev phenomenon for nonconvex variational problems. . Annales de l'Institut Henri Poincare. Analyse Non Lineaire , 22 : 579 – 596 .

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