Hostname: page-component-7479d7b7d-pfhbr Total loading time: 0 Render date: 2024-07-13T19:21:27.099Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on summands of compact convex sets

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Jerzy Grzybowski
Jerzy Grzybowski
Affiliation:
Faculty of Mathematics, Adam Mickiewicz University, ul. Matejki 48/49, 60-769 Poznań, Poland.
Get access

Abstract

In this paper we prove that a maximal common summand of two compact convex sets in R2 is unique up to translation.

MSC classification

Secondary: 52A10: Convex sets in $2$ dimensions (including convex curves)
Type
Research Article
Information
Mathematika , Volume 43 , Issue 2 , December 1996 , pp. 286 - 294
Copyright
Copyright © University College London 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

D-R.Demyanov, V. F. and Rubinov, A. M.. Quasidifferential Calculus (Optimization Software Inc., Springer-Verlag, 1986).CrossRefGoogle Scholar
G.Grzybowski, J.. Minimal pairs of convex compact sets. Archiv der Math., 63 (1994), 173–181.CrossRefGoogle Scholar
P-S-U.Pallaschke, D.Scholtes, S. and Urbanski, R.. On minimal pairs of convex compact sets. Bull. Acad. Polon. Sci., Ser. Sci. Math., 39 (1991), 105–109.Google Scholar
P-U.Pallaschke, D. and Urbanski, R.. Some criteria for the minimality of pairs of convex compact sets. Zeitschrift fur Operations Research, 37 (1993), 129–150.Google Scholar
R-A.Rubinov, A. M. and Akhundov, I. S.. Differences of compact sets in the sense of Demyanov and its application to non-smooth analysis. Optimization 23, (1992), 179–189.CrossRefGoogle Scholar
S1.Scholtes, S.. Minimal pairs of convex bodies in two dimensions, Mathematika, 39 (1992), 267–273.CrossRefGoogle Scholar
S2.Scholtes, S.. On convex bodies and some applications to optimization, Doctoral Thesis (University of Karlsruhe).Google Scholar