Bounded linear regularity of convex sets in Banach spaces and its applications

Mathematical Programming

Volumn 106, Issue 1, 2006, Pages 59-79

  Song, Wen ^a   Zang, Rui ^b  

^a HARBIN NORMAL UNIVERSITY   (China)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

BANACH SPACES; CONICAL HULL INTERSECTION PROPERTY (CHIP); CONVEX SETS;

ERROR ANALYSIS; MATHEMATICAL PROGRAMMING;

SET THEORY;

EID: 29144468040     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-005-0596-1     Document Type: Article

References (30)

1. Aubin, J.P., Ekeland, I.: Applied Nonlinear Analysis. Wiley-lnterscience, New York, 1984
2. Auslener, A.A., Crouzeix, J.P.: Global regularity theorems. Math. Oper. Res. 13, 243-253 (1988)
3. Aze, D., Michel, L.: Computable dual characterization of asympototically well behaved convex function. Comm. Appl. Nonlinear Anal. 6 (1), 39-49 (1999)
4. Bauschke, H.H.: Projection algorithms and monotone operators. PhD thesis, Simon Fraser University, 1996
5. Bauschke, H.H., Borwein, J.M.: On projection algorithms for solving convex feasibility problems. SIAM Review 38, 367-126 (1996)
6. Bauschke, H.H., Borwein, J.M., Li, W.: Strong conical hull intersection property, bounded linear regularity, Jameson's property (G), and error bounds in convex optimization. Math. Program. Ser. A 86, 1135-160 (1999)
7. Bauschke, H.H., Borwein, J.M., Tseng, P.: Metric regualrity, strong CHIP and CHIP are distinct properties. J. Convex Anal. 7, 395-412 (2000)
8. Borwein, J.M., Lewis, A.S.: Partially finite convex programming, part I: quasi relative interiors and duality. Math. Program. Ser.A 57, 15-48 (1992)
9. Borwein, J.M., Lucet, Y., Mordukhovich, B.: Compactly epi-Lischtizian convex sets and functions in normed spaces. J. Conv. Anal. 7, 375-398 (2000)
10. Burke, J., Ferris, M.C., Qian, M.: On the Clarke subdifferential of the distance function of a closed set. J. Math. Anal. Appl. 166, 199-213 (1992)
11. Clarke, F.H.: Optimization and Nonsmooth Analysis. Wiley, New York, 1983
12. Cornejo, O., Jourani, A., Zǎlinescu, C.: Conditioning and uper-Lipshcitz inverse subdifferetial in non-smooth optimization problems. J. Optim. Theory Appl. 95, 127-148 (1997)
13. Deutsch, F., Li, W., Ward, J.D.: A dual approach to constrained interpolation from a convex subset of Hilber space. J. Approx. Theory 90, 385-414 (1997)
14. Deutsch, F., Li, W., Ward, J.D.: Best approximation from the intersection of a closed convex set and a plyhedron in Hubert space, weak Slater conditions, and the strong conical hull intersection property. SIAM J. Optim. 10, 252-268 (1999)
15. Gowda, M.S., Teboulle, M.: A comparison of constraint qualification in infinite-dimensional convex programming. SIAM J. Control Optim. 28, 925-935 (1990)
16. Henrion, R., Jourani, A.: Subdifferential conditions for calmness of convex constraints. SIAM J. Optim. 13, 520-534 (2002)
17. Hiriart-Urruty, J.-B., Lemaréchal, C.: Convex Analysis and Minimization Algorithms. I, Springer-Verlag, Berlin. Fundamentals, 1993
18. Holmes, R.B.: Geometric Functional Analysis and Its Applications. Springer-Verlag, New York, 1975
19. Ioffe, A.: Regular points of Lipschitz functions. Trans. Amer. Math. Soc. 251, 61-69 (1975)
20. Jameson, G.J.O.: The duality of pairs of wedges. Proc. London Math. Soc. 24, 531-547 (1972)
21. Jeyakumar, V: Duality and infinite dimensional optimization. Nonlinear Anal 15, 1111-1122 (1990)
22. Jourani, A.: Intersection formulae and the marginal function in Banach spaces. J. Math. Anal. Appl. 192, 867-891 (1995)
23. Klatte, D., Wu Li: Asymptotic constraint qualifications and global error bounds for convex inequalities. Math. Program. 84, 137-160 (1999)
24. Lewis, A.S., Pang, J.-S.: Error bounds for convex inequality systems. In: J.-P. Crouzeix, et al. (eds.), Proceedings of the 5th International Symposium on Generalized Convexity held in Luminy, June 17-21, 1996, Dordrecht, Kluwer Academic Publishers, pp.75-110, 1998
25. Ng, K.F., Song, W.: Fenchel duality in infinite setting and its applications. Nonlinear Anal 55, 845-858 (2003)
26. Ng, K.F., Yang, W.H.: Regularities and their relations to error bounds. Math. Program. 99, 521-538 (2004)
27. Ng, K.F., Zheng, X.Y.: Error bound for lower semicontinuous functions in normed spaces. SIAM J. Optim. 12, 1-17 (2001)
28. Ponstein, J.: Approaches to the Theory of Optimization. Cambrige Univ. Press, 1980
29. Rockafellar, R.T.: Level sets and continuity of conjugate convex functions. Trans. Amer. Math. Soc. 123, 46-63 (1966)
30. Zalinescu, C.: Convex Analysis in General Vector Spaces, World Scientific, Singapore, 2002