Filters

2008 - 200912010 - 20113

More filters

20194
Reset filters

Settings

Author: Seeger, Alberto × Has files: Yes ×

Search Results

Now showing 1 - 4 of 4
  • Thumbnail Image
    Item
    Uniform boundedness of norms of convex and nonconvex processes
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Henrion, René; Seeger, Alberto
    The lower limit of a sequence of closed convex processes is again a closed convex process. In this note we prove the following uniform boundedness principle: if the lower limit is nonempty-valued everywhere, then, starting from a certain index, the given sequence is uniformly norm-bounded. As shown with an example, the uniform boundedness principle is not true if one drops convexity. By way of illustration, we consider an application to the controllability analysis of differential inclusions.
  • Thumbnail Image
    Item
    Condition number and eccentricity of a closed convex cone
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Henrion, René; Seeger, Alberto
    We discuss some extremality issues concerning the circumradius, the inradius, and the condition number of a closed convex cone in $mathbbR^n$. The condition number refers to the ratio between the circumradius and the inradius. We also study the eccentricity of a closed convex cone, which is a coefficient that measures to which extent the circumcenter differs from the incenter.
  • Thumbnail Image
    Item
    On properties of different notions of centers for convex cones
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Henrion, René; Seeger, Alberto
    The points on the revolution axis of a circular cone are somewhat special: they are the "most interior'' elements of the cone. This paper addresses the issue of formalizing the concept of center for a convex cone that is not circular. Four distinct proposals are studied in detail: the incenter, the circumcenter, the inner center, and the outer center. The discussion takes place in the context of a reflexive Banach space.
  • Thumbnail Image
    Item
    Inradius and circumradius of various convex cones arising in applications
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Henrion, René; Seeger, Alberto
    This note addresses the issue of computing the inradius and the circumradius of a convex cone in a Euclidean space. It deals also with the related problem of finding the incenter and the circumcenter of the cone. We work out various examples of convex cones arising in applications.