New PDF release: Convex Analysis and Its Applications: Proceedings of a

By Marc Atteia, Jacques Audounet (auth.), Alfred Auslender (eds.)

ISBN-10: 3540081496

ISBN-13: 9783540081494

ISBN-10: 3642482988

ISBN-13: 9783642482984

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Additional resources for Convex Analysis and Its Applications: Proceedings of a Conference Held at Murat-le-Quaire, March 1976

Example text

Fan~tionneiie4 Sem~na~~e 4U~ Coiiege de [RJ R. Nume~~que, ~onvexe. Touiou4e 1975-1976. CHATELAIN Queique4 [M] a un integ4ande pai4 Potentie! T. O~ii~z de ~e~tdin4 no~maux. 1975. ~onvexe4. ie4 F~an~e equat~on4 aux de~~vee4 pa~t~eiie4, (muit~g~aph~e). ROCKAFELLAR Integ~ai4 Pa~. de type wh~~h a~e ~onvex J. Math. 24, 1968. 6un~t~onai4 (1). 52 [s1 L. SCHWARTZ Sou~-e~paee~ hilbe4tien~ d'e~paee~ et noyaux a~~oeie~. J. An. Math. Je4u~alem 13, 1964. e';-'e-i--";'---i---i--';'-- .. ;.. veeto4iel~ topologique~ AN ABSTRACT THEOREM FOR PLANNING PROCEDURES by Bernard CORNET* It is shown that any Pareto Optimal program which is prefered or indifferent to the initial program by every agent can be "reached by an abstract monotone planning procedure".

Ainsi que sa semi-continuit€ sup€rieure obtenus par utilisation de r€sultats , B~ est a Cette propri€t€ valeurs de B~ peuvent etre directement classiques d'Analyse Convexe [M], P P 60 e t 7 9 On peut pr€ciser Proposition 9 : davantage la cyclique monotonie de Le noyau d'un potentiel X-coercif r€flexif maximal monotone relativement D €mons tr at ion a la dualit€ . I doom..... t. e I · L a e s que eo'f" o 37 fonctionnelle e definie sur X' par e(e ' ) = ~~(el) - X n'est pas minimale en e e I appartient alors 1 a 0 dom So it done ej ~f.

Enfin, Ecjl etant reflexif, l'espace engendre par Bcjl X' est dense dans Ecjl' Remarque : Si cjl n'est pas reflexif, on etablit de maniere analogue, la densite de l'espace engendre par Bcjl X' dans Ecjl muni de la topo--E-t logie O(Ecjl' tjcjl X' cjl ). La partie Bcjl X' de Ecjl est l'assise de la fonctionnelle cjl dans la dualite (X, X') ; un element jcjl x de X appartient si et seulement si h + a cjl(x+h) est sous-differentiable dans la dualite (Ecjl' X'). Cette caracterisation, jointe a Bcjl X' l'origine a Proposition 9, redonne dans Ie cas hilbertien la proposition 7 de [SJ.

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Convex Analysis and Its Applications: Proceedings of a Conference Held at Murat-le-Quaire, March 1976 by Marc Atteia, Jacques Audounet (auth.), Alfred Auslender (eds.)


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