Computable error bounds for convex inequality systems in reflexive banach spaces

SIAM Journal on Optimization

Volumn 7, Issue 1, 1997, Pages 274-279

  Deng, Sien ^a  

^a NORTHERN ILLINOIS UNIVERSITY   (United States)

Author keywords

Error bounds; Recession cones; Recession functions

Indexed keywords

EID: 0031538926     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623495284832     Document Type: Article

References (18)

1. A. A. AUSLENDER AND J.-P. CROUZEIX, Global regularity theorems, Math. Oper. Res., 13 (1988), pp. 243-253.
2. J. P. AUBIN, Optima and Equilibria, Springer-Verlag, Berlin, New York, 1993.
3. M. M. DAY, Normed Linear Spaces, Springer-Verlag, Berlin, New York, 1973.
4. M. S. GOWDA, An analysis of zero set and global error bound properties of a piecewise affine function via its recession, function, SIAM J. Matrix Anal. Appl., 17 (1996), pp. 594-009.
5. A. J. HOFFMAN, On approximate solutions of systems of linear inequalities, J. Res. Nat. Bur. Standards, 49 (1952), pp. 263-265.
6. H. HU AND Q. WANG, On approximate solutions of infinite systems of linear inequalities, Linear Algebra Appl., 114/115 (1989), pp. 429-438.
7. W. LI, Error bounds for pircewise convex quadratic programs and applications, SIAM J. Control Optim., 33 (1995), pp. 1510-1529.
8. X.-D. LUO AND Z.-Q. LUO, Extension of Hoffman's error bound to polynomial systems, SIAM J. Optim., 4 (1994), pp. 383-392.
9. Z. Q. LUO AND J. S. PANG. Error bounds for analytic, systems and their applications, Math. Programming 67 (1995). pp. 1-28.
10. A. D. IOFFE AND V. M. TIHOMIROV, Theory of Extremal Problems, Nauka, Moscow, 1974 (in Russian).
11. A. D. IOFFE, Regular points of Lipschitz functions, Trans. Amer. Math. Soc., 251 (1979), pp. 61-69.
12. O. L. MANGASARIAN, A condition number for differentiable convex inequalities, Math. Oper. Res., 10 (1985), pp. 175-179.
13. R. MATHIAS AND J. S. PANG, Error bounds for the linear complementarity problem with a P-matrix, Linear Algebra Appl., 132 (1990), pp. 123-136.
14. S. M. ROBINSON, An application of error bounds for convex programming in a linear space, SIAM J. Control, 13 (1975), pp. 271-273.
15. R. T. ROCKAFELLAR, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
16. R. T. ROCKAFELLAR, Level sets and continuity of conjugate convex functions, Trans. Amer. Math. Soc., 123 (1966), pp. 46-63.
17. T. WANG AND J. S. PANG, Global error bounds for convex quadratic inequality systems, Optimization, 31 (1994), pp. 1-12.
18. J. V. BURKE AND P. TSENG, A unified analysis of Hoffman's bound via Fenchel duality, SIAM J. Optim., 6 (1996), pp. 265-282.