Set-Valued Analysis

, Volume 4, Issue 2, pp 135–155

Cutting and scanning methods in set-valued analysis I. An epigraphical and graphical calculus

  • H. Attouch
  • M. Volle

DOI: 10.1007/BF00425962

Cite this article as:
Attouch, H. & Volle, M. Set-Valued Anal (1996) 4: 135. doi:10.1007/BF00425962


Cutting analysis of sets (scanning, laser exploration, etc.), when applied to epigraphs of functions and graphs of operators, gives rise to a rich calculus and provides a unifying approach to various operations in optimization and variational analysis.

Mathematics Subject Classifications (1991)

41A65 65K10 

Key words

epigraphical analysis cutting methods scanning analysis slice sublevel sets epigraphical sum sublevel sum convexity quasi-convexity parallel sum of operators 

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • H. Attouch
    • 1
  • M. Volle
    • 2
  1. 1.Département des Sciences mathématiquesUniversité Montpellier 2Montpellier Cedex 5France
  2. 2.Département de MathématiquesUniversité d'AvignonAvignonFrance

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