[en] Attouch and Wets have introduced recently a variational metric between closed proper convex functions. The aim of this note is to give an estimation of this metric in the case of the exponential penalties. We can therefore recover some convergence results for the exponential penalty method.
Disciplines :
Mathematics
Author, co-author :
Mouallif, Khalil
Tossings, Patricia ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Mathématiques générales
Murphy F. (1974) A Class of Exponential Penalty Functions. SIAM Journal on Control 12:679-687.
Attouch H., Wets R. (1986) Isometries for the Legendre-Fenchel Transform. Transactions of the American Mathematical Society 296:33-60.
Brezis H. Opérateurs Maximaux Monotones et Semigroupes de Contractions dans les Espaces de Hilbert, North-Holland, Amsterdam, Holland; 1973.
Attouch H. Variational Convergence for Functions and Operators, Pitman, New York, New York; 1984.
Aubin J.P. L'Analyse Nonlinéaire et ses Motivations Economiques, Masson, Paris, France; 1984.
Rockafellar R.T. Convex Analysis, Princeton University Press, Princeton, New Jersey; 1970.
Rockafellar R.T. (1976) Monotone Operators and the Proximal Point Algorithm. SIAM Journal on Control and Optimization 14:877-896.
Ekeland I., Temam R. Analyse Convexe et Problèmes Variationnels, Dunod-Gauthier-Villars, Paris, France; 1974.
Lemaire B. Coupling Optimization Methods and Variational Convergence: Trends in Mathematical Optimization , K. H., Hoffmann, J. B., Hiriart-Urruty, C., Lemarechal, J., Zowe, Birkhaüser Verlag, Basel, Switzerland; 1988, 163-179.
Mouallif K., Tossings P. (1987) Une Méthode de Pénalisation Exponentielle Associée à une Régularisation Proximale. Bulletin de la Société Royale des Sciences de Liège 56:181-192.
