Convergence en niveaux et en épigraphes. (Convergences by epigraph and level set methods.). (French) Zbl 0566.49004

Volle, Michel

C. R. Acad. Sci., Paris, Sér. I 299, 295-298 (1984).

Two convergence notions for relations are introduced, which agree for monotone relations. In the particular case of level sets of functions, a characterization of epi-convergence is obtained. An application to quasi- inf-convolution is presented.

Reviewer: T.Zolezzi

MSC:

49J45	Methods involving semicontinuity and convergence; relaxation
49K40	Sensitivity, stability, well-posedness
54A20	Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
26E25	Set-valued functions
54C60	Set-valued maps in general topology

Keywords:

convergence notions for relations; level sets; epi-convergence; quasi- inf-convolution