Minimal Fractions of Compact Convex Sets

  • D. Pallaschke
  • R. Urbański
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 79)


Pairs of compact convex sets naturally arise in quasidifferential calculus as sub- and super-differentials of a quasidifferentiable function (see [1]). Since the sub- and superdifferential are not uniquely determined, minimal representations are of special importance. In this paper we show that the problem of finding minimal representatives for the elements of pairs of compact convex sets is a special case of the more general problem of determining minimal fractions in ordered commutative semigroups which satisfy the order cancellation law. All the material of this paper is taken from the recently published textbook on pairs of compact convex sets ([11]).

Key words

quasidifferentiable function pairs of compact convex sets 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • D. Pallaschke
    • 1
  • R. Urbański
    • 2
  1. 1.Institut für Statistik und Mathematische WirtschaftstheorieUniversität KarlsruheKarlsruheGermany
  2. 2.Wydzal Matematyki i InformatykiUniwersytet im Adama MickiewiczaPoznańPoland

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