Eigenvalue-constrained faces

Linear Algebra and Its Applications

Volumn 269, Issue 1-3, 1998, Pages 159-181

  Lewis, A S ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041856546     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(97)81515-7     Document Type: Article

References (19)

1. F. Alizadeh, J.-P. A. Haeberly, and M. L. Overton, Complementarity and nondeneracy in semidefinite programming, Math. Programming, Series B 77:111-128 (1997).
2. G. P. Barker and D. Carlson, Cones of diagonally dominant matrices, Pacafic J. Math. 57:15-32 (1975).
3. E. M. de Sá, Exposed faces and duality for symmetric and unitarily invariant norms, Linear Algebra Appl. 197-198:429-450 (1994).
4. E. M. de Sá, Faces of the unit ball of a symmetric gauge function, Linear Algebra Appl. 197-198:349-395 (1994).
5. E. M. de Sá, Faces of the unit ball of a unitarily invariant norm, Linear Algebra Appl. 197-198:451-493 (1994).
6. M. Fiedler and V. Pták, Diagonal of convex sets, Czechoslovak Math. J. 28:25-44 (1978).
7. P. A. Fillmore and J. P. Williams, Some convexity theorems for matrices, Glasgow Math. J. 12:110-117 (1971).
8. A. S. Lewis, The convex analysis of unitarily invariant matrix functions, J. Convex Anal. 2:173-183 (1995).
9. A. S. Lewis, Von Neumann's Lemma and a Chevalley-Type Theorem for Convex Functions on Cartan Subspaces, Technical Report CORR 95-19, University of Waterloo, 1995; Nonlinear Analysis, submitted for publication.
10. A. S. Lewis, Convex analysis on the Hermitian matrices, SIAM J. Optim. 6:164-177 (1996).
11. A. S. Lewis, Group invariance and convex matrix analysis, SIAM J. Matrix Anal. Appl. 17:927-949 (1996).
12. A. L. Onishchik and E. B. Vinberg, Lie Groups and Algebraic Groups, Springer-Verlag, Berlin, 1990.
13. G. Pataki, On Cone-LP's and Semi-definite Programs: Facial Structure, Basic Solutions and the Simplex Method, Technical Report GSIA 1995-03, Carnegie Mellon Univ., 1995.
14. M. Ramana, L. Tunçel, and H. Wolkowicz, Strong duality for semidefinite programming, SIAM J. Optim. 7:641-662 (1997).
15. R. T. Rockafellar, Convex Analysis, Princeton U.P., Princeton, N. J. 1970.
16. C. H. Sung and B. S. Tam, A study of projectionally exposed cones, Linear Algebra Appl. 139:225-252 (1990).
17. B. S. Tam, On the structure of the cone of positive operators, Linear Algebra Appl. 167:65-85 (1992).
18. B. S. Tam and H. Schneider, On the core of a cone-preserving map, Trans. Amer. Math. Soc. 343:479-524 (1994).
19. O. Taussky, Positive-definite matrices and their role in the study of characteristic roots of general matrices, Adv. Math. 2:175-186 (1968).