Antipodal pairs, critical pairs, and Nash angular equilibria in convex cones

Optimization Methods and Software

Volumn 23, Issue 1, 2008, Pages 73-93

  Iusem, Alfredo ^a   Seeger, Alberto ^b  

^a IMPA   (Brazil)

^b UNIVERSITY OF AVIGNON   (France)

Author keywords

Antipodal pairs; Convex cones; Critical angle; Maximal angle; Nash angular equilibria; Polyhedral cones

Indexed keywords

ANGLE MEASUREMENT; PROBLEM SOLVING;

ANTIPODAL PAIRS; CONVEX CONES; CRITICAL ANGLE; MAXIMAL ANGLE; NASH ANGULAR EQUILIBRIA; POLYHEDRAL CONES;

COMPUTATIONAL GEOMETRY;

EID: 37549018556     PISSN: 10556788     EISSN: 10294937     Source Type: Journal    
DOI: 10.1080/10556780701661427     Document Type: Article

References (10)

1. C. Berge, Espaces Topologiques, Fonctions Multivoques, Dunod, Paris, 1966.
2. G.H. Golub and C.F. Van Loan, Matrix Computations. John Hopkins University Press, Baltimore, 1996.
3. A. Iusem and A. Seeger, On pairs of vectors achieving the maximal angle of a convex cone, Math. Program. 104 (2005), pp. 501-523.
4. _, Axiomatization of the index of pointedness for closed convex cones, Comput. Appl. Math. 24 (2005), pp. 245-283.
5. _, Angular analysis of two classes of non-polyhedral convex cones: the point of view of optimization theory, Comp. Appl. Math. 26 (2007), pp. 191-214.
6. _, Searching for critical angles in a convex cone, Math. Program., (2008), in press. Available at doi: 10.1007/s10107-007-0146-0.
7. J. Nash, Non-cooperative games, Ann. Math. 54 (1951), pp. 286-295.
8. J. Peña and J. Renegar, Computing approximate solutions for conic systems of constraints, Math. Program. 87 (2000), pp. 351-383.
9. R.T. Rockafellar and R.J. Wets, Variational Analysis, Springer-Verlag, Berlin, 1998.
10. D.W. Walkup and R.J.B. Wets, Continuity of some convex-cone-valued mappings, Proc. Amer. Math. Soc. 18 (1967), pp. 229-235.