Characterization of the barrier parameter of homogeneous convex cones

Mathematical Programming, Series B

Volumn 81, Issue 1, 1998, Pages 55-76

  Güler, Osman ^a,b   Tunçel, Levent ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

^b UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

Author keywords

Barrier functions; Carath odory number; Homogeneous cones; Rank; Self concordance; Siegel domain

Indexed keywords

EID: 0038929317     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01584844     Document Type: Article

References (18)

1. J. Dorfmeister, Homogeneous Siegel domains, Nagoya Math. J. 86 (1982) 39-83.
2. J. Faraut and A. Korányi, Analysis on Symmetric Cones (Oxford University Press, New York, 1994).
3. L. Faybusovich, Jordan algebras, symmetric cones and interior-point methods, Manuscript, Dept. of Mathematics, University of Notre Dame, IN, USA, 1995.
4. S.G. Gindikin, Analysis in homogeneous domains, Russian Math. Surveys 19 (1964) 1-89.
5. S.G. Gindikin, Tube domains and the Cauchy problem, Translation of Mathematical Monographs, Vol. 111 (AMS Providence, RI, 1992).
6. O. Güler, Barrier functions in interior point methods, Mathematics of Operations Research 21 (1996) 860-885.
7. O. Güler and L. Tunçel, Invariant barrier functions on homogeneous convex cones, in preparation.
8. A. Krieg, Modular Forms on Half-Spaces of Quaternions, Lecture Notes in Mathematics, Vol. 1143 (Springer, New York, 1985).
9. A.S. Nemirovskii, Private communication, 1995.
10. Yu.E. Nesterov and A.S. Nemirovskii, Interior-Point Polynomial Algorithms in Convex Programming (SIAM Publications, Philadelphia, PA, 1994).
11. Yu.E. Nesterov and M.J. Todd, Self-scaled barriers and interior-point methods for convex programming, Mathematics of Operations Research 22 (1997) 1-46.
12. Yu.E. Nesterov and M.J. Todd, Primal-dual interior-point methods for self-scaled cones, SIAM Journal on Optimization (1997), to appear.
13. M. Ramana, L. Tunçel and H. Wolkowicz, Strong duality for semidefinite programming, SIAM Journal on Optimization (1997), to appear.
14. O.S. Rothaus, Domains of Positivity. Abh. Math. Sem. Univ. Hamburg 24 (1960) 189-235.
15. O.S. Rothaus, The construction of homogeneous convex cones, Annals of Math. 83 (1966) 358-376.
16. R. Schneider, Convex Bodies: The Brunn-Minkowski Theory (Cambridge University Press, Cambridge, UK, 1993).
17. È.B. Vinberg, The theory of homogeneous cones, Trans. Moscow Math. Soc. 12 (1965) 340-403.
18. È.B. Vinberg, The structure of the group of automorphisms of a homogeneous convex cone, Trans. Moscow Math. Soc: 13 (1965) 63-93.