Error bounds for abstract linear inequality systems

SIAM Journal on Optimization

Volumn 13, Issue 1, 2003, Pages 24-43

  Ng, Kung Fu ^a   Yang, Wei Hong ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

"Ice cream" cone; Abstract linear inequality system; Angles between subspaces; Error bound; Polyhedral cone

Indexed keywords

EID: 0037288592     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/s1052623401388914     Document Type: Article

References (16)

1. J. M. BORWEIN, S. P. FITZPATRICK, AND J. R. GILES, The differentiability of real functions on normed linear space using generalized subgradients, J. Math. Anal. Appl., 128 (1987), pp. 512-534.
2. J. V. BURKE AND P. TSENG, A unified analysis of Hoffman's bound via Fenchel duality, SIAM J. Optim., 6 (1996), pp. 265-282.
3. F. H. CLARKE, Optimization and Nonsmooth Analysis, Wiley, New York, 1983.
4. F. DEUTSCH, The angle between subspaces of a Hilbert space, in Approximation Theory, Wavelets and Applications, S. P. Singh, ed., Kluwer Academic Publishers, Norwell, MA, 1995, pp. 107-130.
5. Y. R. HE, Error Bound for Nonlinear Complementarity Problems, preprint, The Chinese University of Hong Kong, Shatin, Hong Kong, 2000.
6. J.-B. HIRIART-URRUTY AND C. LEMARÉCHAL, Convex Analysis and Minimization Algorithms I, Springer-Verlag, New York, 1993.
7. A. J. HOFFMAN, On approximate solutions of systems of linear inequalities, J. Res. National Bureau of Standards, 49 (1952), pp. 263-265.
8. A. D. IOFFE, Regular points of Lipschitz functions, Trans. Amer. Math. Soc., 251 (1979), pp. 61-69.
9. A. LEWIS AND J.-S. PANG, Error bounds for convex inequality systems, in Generalized Convexity, Generalized Monotonicity. Proceedings of the Fifth Symposium on Generalized Convexity, Luminy, 1996, J.-P. Crouzeix, J.-E. Martinez-Legaz, and M. Volle, eds., Nonconvex Optim. Appl. 27, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997, pp. 75-100.
10. K. F. NG AND X. Y. ZHENG, Error bounds for lower semicontinuous functions in normed spaces, SIAM J. Optim., 12 (2001), pp. 1-17.
11. K. F. NG AND X. Y. ZHENG, Global Weak Sharp Minima on Banach Spaces, preprint, The Chinese University of Hong Kong, Shatin, Hong Kong, 2001.
12. J.-S. PANG, Error bounds in mathematical programming, Math. Programming, 79 (1997), pp. 299-332.
13. R. R. PHELPS, Convex Functions, Monotone Operators and Differentiability, Springer-Verlag, Berlin, Heidelberg, 1989.
14. S. M. ROBINSON, Stability theory for systems of inequalities. Part I: Linear systems, SIAM J. Numer. Anal., 12 (1975), pp. 754-769.
15. R. T. ROCKAFELLAR, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
16. S. ZHANG, Global error bounds for convex conic problems, SIAM J. Optim., 10 (2000), pp. 836-851.