140
CHAPITRE 5 DUALISATION, CAS NON CONVEXES
Références
[BHU] J. Benoist and J.-B. Hiriart-Urruty. "What is the subdifferential of
the closed convex hull of a function ?". SIAM J. Math. Anal. Vol. 27, 6
(1996), p. 1661–1679.
[B] B. Brighi. "Sur l’enveloppe convexe d’une fonction de la variable
réelle". Revue de Mathématiques Spéciales 8 (1994), p. 547–550.
[L] Y. Lucet. "What shape is your conjugate ? A survey of computational
convex analysis and its applications". SIAM J. on Optimization Vol. 20,
1 (2009), p. 216–250.
[HULV] J.-B. Hiriart-Urruty, M. Lopez and M. Volle. "The ε-strategy in
variational analysis : illustration with the closed convex convexification
of a function". Revista Matemática, Iberoamericana 27(2), 2011, pp.
449–471.
[ET] I. Ekeland and T. Turnbull. Infinite-Dimensional Optimization and
Convexity. Chicago Lectures in Mathematics Series, 1983.
[T1] J.F. Toland. "Duality in nonconvex optimization". J. Math. Anal. Appl.
66 (1978), p. 399–415.
[T2] J.F. Toland. "A duality principle for non-convex optimisation and the
calculus of variations". Arch. Rational Mech. Anal. 71 (1979), p. 41–61.
[AT] H. Attouch and M. Théra. "A general duality principle for the sum of
two operators". J. of Convex Anal. Vol. 3, 1 (1996), p. 1–24.
[EL] I. Ekeland and J.-M. Lasry. "Problèmes variationnels non convexes en
dualité". Note aux CRAS Paris 290 (1980), P. 493–496.
[E] I. Ekeland. Convexity Methods in Hamiltonian Mechanics. Springer
Verlag, 1990.
[S] I. Singer. "A Fenchel-Rockafellar type duality theorem for maximization". Bull. Australian Math. Soc. 20 (1979), p. 193–198.
[HU] J.-B. Hiriart-Urruty. "A general formula on the conjugate of the difference of functions". Canad. Math. Bull. Vol. 29, 4 (1986), p. 482–485.
CHAPITRE 5 DUALISATION, CAS NON CONVEXES
Références
[BHU] J. Benoist and J.-B. Hiriart-Urruty. "What is the subdifferential of
the closed convex hull of a function ?". SIAM J. Math. Anal. Vol. 27, 6
(1996), p. 1661–1679.
[B] B. Brighi. "Sur l’enveloppe convexe d’une fonction de la variable
réelle". Revue de Mathématiques Spéciales 8 (1994), p. 547–550.
[L] Y. Lucet. "What shape is your conjugate ? A survey of computational
convex analysis and its applications". SIAM J. on Optimization Vol. 20,
1 (2009), p. 216–250.
[HULV] J.-B. Hiriart-Urruty, M. Lopez and M. Volle. "The ε-strategy in
variational analysis : illustration with the closed convex convexification
of a function". Revista Matemática, Iberoamericana 27(2), 2011, pp.
449–471.
[ET] I. Ekeland and T. Turnbull. Infinite-Dimensional Optimization and
Convexity. Chicago Lectures in Mathematics Series, 1983.
[T1] J.F. Toland. "Duality in nonconvex optimization". J. Math. Anal. Appl.
66 (1978), p. 399–415.
[T2] J.F. Toland. "A duality principle for non-convex optimisation and the
calculus of variations". Arch. Rational Mech. Anal. 71 (1979), p. 41–61.
[AT] H. Attouch and M. Théra. "A general duality principle for the sum of
two operators". J. of Convex Anal. Vol. 3, 1 (1996), p. 1–24.
[EL] I. Ekeland and J.-M. Lasry. "Problèmes variationnels non convexes en
dualité". Note aux CRAS Paris 290 (1980), P. 493–496.
[E] I. Ekeland. Convexity Methods in Hamiltonian Mechanics. Springer
Verlag, 1990.
[S] I. Singer. "A Fenchel-Rockafellar type duality theorem for maximization". Bull. Australian Math. Soc. 20 (1979), p. 193–198.
[HU] J.-B. Hiriart-Urruty. "A general formula on the conjugate of the difference of functions". Canad. Math. Bull. Vol. 29, 4 (1986), p. 482–485.