Error Bound Moduli for Conic Convex Systems on Banach Spaces

References

• Aubin J-P., Frankowska H.Set-Valued Analysis (1990) (Birkhäuser Boston Inc., Boston, MA) Google Scholar
• Day M. M.Normed Linear Spaces (1962) (Springer-Verlag, Berlin, Germany) Crossref, Google Scholar
• Deng S. Global error bounds for convex inequality systems in Banach spaces. SIAM J. Control Optim. (1998) 36:1240–1249Crossref, Google Scholar
• He Y. R. Error bounds for nonlinear complementarity problems. (2001) . PreprintGoogle Scholar
• Hoffman A. J. On approximate solutions of systems of linear inequalities. J. Res. National Bureau Standards (1952) 49:263–265Crossref, Google Scholar
• Jameson G.Ordered Linear Spaces (1970) (Springer-Verlag, Berlin) Crossref, Google Scholar
• Jourani A. Hoffman's error bound, local controlability and sensitivity analysis. SIAM J. Optim. (2000) 38:947–970Crossref, Google Scholar
• Klatte D., Li W. Asymptotic constraint qualifications and error bounds for convex inequalities. Math. Programming (1999) 84:137–160Crossref, Google Scholar
• Lewis A., Pang J. S., Crouzeix J-P., Martinez-Legaz J-E., Volle M. Error bounds for convex inequality systems. Generalized Convexity, Generalized Monotonicity: Recent Results, Proc. Fifth Sympos. on Generalized Convexity (1997) June 1996Luminy(Kluwer Academic Publishers, Dordrecht, The Netherlands) 75–100Google Scholar
• Li W. Abadie's constraint qualification, metric regularity, and error bounds for differentiable convex inequalities. SIAM J. Optim. (1997) 7:966–978Crossref, Google Scholar
• Luo X. D., Luo Z. Q. Extensions of Hoffman's error bound to polynomial systems. SIAM J. Optim. (1994) 4:383–392Crossref, Google Scholar
• Mangasarian O. L. A condition number for differentiable convex inequalities. Math. Oper. Res. (1985) 10:175–179Link, Google Scholar
• Ng K. F., Yang W. H. Error bounds for abstract linear systems. SIAM J. Optim. (2002) 13:24–43Crossref, Google Scholar
• Ng K. F., Zheng X. Y. Error bounds for lower semicontinuous functions in normed spaces. SIAM J. Optim. (2001) 12:1–17Crossref, Google Scholar
• Ng K. F., Zheng X. Y. Characterizations of error bounds for convex multifunctions on Banach spaces. Math. Oper. Res. (2004) 29:45–63Link, Google Scholar
• Phelps R. R.Convex Functions, Monotone Operators and Differentiability (1993) (Springer-Verlag, Berlin, Germany) Google Scholar
• Wu Z. L., Ye J. J. Sufficient conditions for error bounds. SIAM J. Optim. (2001) 12:421–435Crossref, Google Scholar
• Wu Z. L., Ye J. J. On error bounds for lower semicontinuous functions. Math. Programming (2002) 92(2):301–314Crossref, Google Scholar
• Zalinescu C. Weak sharp minima, well-behaving functions and global error bounds for convex inequalities in Banach spaces. Proc. 12th Baikal Internat. Conf. on Optimization Methods and Their Appl. (2001) Irkutsk, Russia:272–284Google Scholar
• Zalinescu C.Convex Analysis in General Vector Spaces (2002) (World Scientific, Singapore) Crossref, Google Scholar
• Zheng X. Y. A series of convex functions on a Banach space. Acta Mathematica Sinica (1998) 41:19–28Google Scholar
• Zheng X. Y. Error bounds for set inclusions. Sci. China Ser. A (2003) 46:750–763Crossref, Google Scholar