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)


Key words

epigraphical analysiscutting methodsscanning analysisslicesublevel setsepigraphical sumsublevel sumconvexityquasi-convexityparallel 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