Antipodality in convex cones and distance to unpointedness

Applied Mathematics Letters

Volumn 21, Issue 10, 2008, Pages 1018-1023

  Iusem, Alfredo ^a   Seeger, Alberto ^b  

^a IMPA   (Brazil)

^b UNIVERSITY OF AVIGNON   (France)

Author keywords

Antipodality; Convex cone; Distance to unpointedness

Indexed keywords

ANTIPODALITY; CONVEX CONE; CONVEX CONES; DISTANCE TO UNPOINTEDNESS; HAUSDORFF DISTANCE;

CONES;

EID: 48849089817     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2007.10.018     Document Type: Article

References (7)

1. Iusem A., and Seeger A. On pairs of vectors achieving the maximal angle of a convex cone. Math. Program. 104 (2005) 501-523
2. Iusem A., and Seeger A. Axiomatization of the index of pointedness for closed convex cones. Comput. Appl. Math. 24 (2005) 245-283
3. Iusem A., and Seeger A. Measuring the degree of pointedness of a closed convex cone: A metric approach. Math. Nachr. 279 (2006) 599-618
4. Iusem A., and Seeger A. Computing the radius of pointedness of a convex cone. Math. Program. 111 (2008) 217-241
5. A. Iusem, A. Seeger, Searching for critical angles in a convex cone, Math. Program., 2008 (in press), available online at: 10.1007/s10107-007-0146-0
6. Rockafellar R.T., and Wets R.J.B. Variational Analysis (1998), Springer-Verlag
7. Walkup D.W., and Wets R.J.B. Continuity of some convex-cone-valued mappings. Proc. Amer. Math. Soc. 18 (1967) 229-235