Inf-convolution quasi-convexe des fonctionnelles positives. (Quasi-convex inf-convolution of positive functionals). (French) Zbl 0783.49008

Elqortobi, Abdelkader

RAIRO, Rech. Opér. 26, No. 4, 301-311 (1992).

Summary: The infimal convolution has an important role in convex analysis. It is closely related to a polar of a convex function. We use the definition of a quasiconvex infimal convolution to define our polar which is related to the polars defined respectively by J. P. Crouzeix [‘Contributions à l’étude des fonctions quasiconvexes’, Thèse de Doctorat d’État, Série E, No. d’Ordre 250 (1977), Univ. de Clermont-Ferrand] and H. J. Greenberg and W. P. Pierskalla [Cah. Centre Etudes Rech. Oper. 15, 437-448 (1973; Zbl 0276.90051)]. In this work, we shall define its quasi-tangential and we shall end by an example: the “surrogate duality”.

MSC:

49J52

Nonsmooth analysis

Keywords:

quasiconvexity; surrogate duality; infimal convolution; convex analysis; quasiconvex infimal convolution; quasi-tangential

Citations:

Zbl 0276.90051