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Języki publikacji
Abstrakty
In this paper, we first establish both primal (involving directional derivatives and tangent cones) and dual characterizations (involving subdifferential and normal cones) for the local (global) error bounds of constrained set-valued systems; as an application, we then derive both primal and dual characterizations for the local (global) error bounds of the constrained convex inequality systems in a general Banach space and also some sufficient conditions. The obtained results improve or generalize some known results.
Czasopismo
Rocznik
Tom
Strony
775--792
Opis fizyczny
Bibliogr. 33 poz.
Twórcy
autor
- Department of Mathematics, Harbin Normal University, Harbin 150080, China
Bibliografia
- BONNANS, J.F. and SHAPIRO, A. (2000) Perturbation Analysis of Optimization Problems. Springer Series in Operations Research, Springer-Verlag, New York.
- BURKE, J.V. and FERRIS, M.C. (1993) Weak sharp minima in mathematical programming. SIAM J. Control. Optim. 31, 1340-1359.
- BURKE, J.V. and DENG, S. (2002) Weak sharp minima revisited. Part I: basic theory. Control and Cybernetics, 31, 439-470.
- BURKE, J. V. and DENG, S. (2005) Weak sharp minima revisited. Part II: application to linear regularity and error bounds. Math. Program. 104, 235-261.
- URKE, J., FERRIS, M. C. and QIAN, M. (1992) On the Clarke subdifferential of the distance function of a closed set. J. Math. Anal. Appl. 166, 199-213.
- BURKE, J. V. and TSENG, P. (1996) A unified analysis of Hoffman’s bound via Fenchel duality. SIAM J. Optim. 6, 265-282.
- DENG, S. (1998) Global error bounds for convex inequality systems in Banach spaces. SIAM J. Control and Optim. 36, 1240-1249.
- DONTCHEV, A. L. and ROCKAFELLAR, R. T. (2004) Regularity and conditioning of solution mappings in variational analysis. Set-Valued Anal. 12, 79-109.
- FERRIS, M. C. (1988) Weak sharp minima and penalty functions in mathematical programming. PhD Thesis, University of Cambridge.
- HENRION R. and JOURANI, A. (2002) Subdifferential conditions for calmness of convex constraints. SIAM J. Optim. 13, 520-534.
- HENRION, R., JOURANI, A. and OUTRATA, J. (2002) On the calmness of a class of multifunctions. SIAM J. Optim. 13, 603-618.
- HENRION, R. and OUTRATA, J. (2001) A subdifferential condition for calmness of multifunctions. J. Math. Anal. Appl. 258, 110-130.
- HENRION, R. and OUTRATA, J. (2005) Calmness of constraint systems with applications. Math. Program. 104, 437-464.
- HOFFMAN, A. J. (1952) On approximate solutions of systems of linear inequalities. J. Research Nat. Bur. Standards 49, 263-265.
- IOFFE, A. (1975) Regular points of Lipschitz functions. Trans. Amer. Math. Soc. 251, 61-69.
- JEYAKUMAR, V., SONG, W., NINH N. and LEE, G.M. (2005) Stable strong duality in convex optimization. Applied Mathematics, preprint, University of New South Wales, Sydney.
- KLATTE D. and LI, W. (1999) Asymptotic constraint qualifications and global error bounds for convex inequalities. Math. Program. 84, 137-160.
- LEWIS, A.S. and PANG, J.S. (1998) Error bounds for convex in equality systems. In: J. -P. Crouzeix, J. -E. Martinez-Legaz and M. Voile, eds., Proceedings of the 5th International Symposium on Generalized Convexity, Luminy, 1996, Kluwer Academic Publishers, Dordrecht, 75-110.
- LI, W. and SINGER, I. (1998) Global error bounds for convex multifunctions and applications. Math. Oper. Res. 23, 443-462.
- MORDUKHOVICH, B.S., NAM, N.M. and YEN, N.D. (2007) Subgradients of marginal functions in parametric mathematical programming. Math. Program, online first: 10.1007/sl0107-007-0120-x.
- NG, K.F. and YANG, W.H. (2002) Error bounds for abstract linear inequality systems. SIAM J. Optim. 13, 24-43.
- NG, K.F. and ZHENG, X.Y. (2001) Error bound for lower semicontinuous functions in normed spaces. SIAM J. Optim. 12, 1-17.
- NG, K.F. and ZHENG, X.Y. (2004) Characterizations of error bounds for convex multifunctions on Banach spaces. Math. Oper. Res. 29, 45-63.
- ROBINSON, S. (1976) Regularity and stability for convex multivalued functions. Math. Oper. Res. 1, 1130-143.
- SONG, W. (2006) Calmness and error bounds for convex constrained systems. SIAM J. Optim. 17, 353-371.
- SONG, W. and ZANG, R. (2006) Bounded linear regularity of convex sets in Banach spaces. Math. Program. 106, 59-79.
- STUDNIARSKI M. and WARD, D.E. (1999) Weak sharp minima: characterizations and sufficient conditions. SIAM J. Control Optim. 38, 219-236.
- TRUONG, X.D.H. (2005) Lagrange multipliers for set-valued problems associated with coderivatives. J. Math. Anal. Appl. 311, 647-663.
- WU, Z. and YE, J.J. (2003) First-order and second order conditions for error bounds. SIAM J. Optim. 14 , 621-645.
- ZALINESCU, C. (2002) Convex Analysis in General Vector Spaces. World Scientific, Singapore,
- ZHENG, X.Y. and NG, K.F. (2003) Metric regularity and constraint qualifications for convex inequalities on Banach spaces. SIAM J. Optim. 14, 757-772.
- ZHENG, X.Y. and NG, K.F. (2007) Metric subregularity and constraint qualifications for convex generalized equations in Banach spaces. SIAM J. Optim. 18, 437-460.
- ZHENG, X.Y. (2003) Error bounds for set inclusions. Science in China, Series A, 46, 750-763.
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Bibliografia
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bwmeta1.element.baztech-article-BAT5-0017-0067