Strong conical hull intersection property, bounded linear regularity, Jameson's property (G), and error bounds in convex optimization

Mathematical Programming, Series B

Volumn 86, Issue 1, 1999, Pages 135-160

  Bauschke, Heinz H ^a   Borwein, Jonathan M ^b   Li, Wu ^c  

^a OKANAGAN UNIVERSITY COLLEGE   (Canada)

^b SIMON FRASER UNIVERSITY   (Canada)

^c OLD DOMINION UNIVERSITY   (United States)

Author keywords

Angle; Asymptotic constraint qualification; Basic constraint qualification; Bounded linear regularity; CHIP; Conical hull intersection property; Constrained best approximation; Convex feasibility problem; Convex inequalities; Error bound; Friedrichs angle

Indexed keywords

EID: 0001030731     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s101070050083     Document Type: Article

References (35)

1. Auslender, A.A., Crouzeix, J.-P. (1988): Global regularity theorems. Math. Oper. Res. 13, 243-253
2. Bauschke, H.H. (1996): Projection Algorithms and Monotone Operators. PhD thesis, Simon Fraser University, Department of Mathematics, Burnaby, British Columbia V5A 1S6, Canada Available at http://www.cecm.sfu.ca/preprints/1996pp.html
3. Bauschke, H.H., Borwein, J.M. (1993): On the convergence of von Neumann's alternating projection algorithm for two sets. Set-Valued Anal. 1, 185-212
4. Bauschke, H.H., Borwein, J.M. (1993): On projection algorithms for solving convex feasibility problems. SIAM Rev. 38, 367-126
5. Bauschke, H.H., Borwein, J.M., Lewis, A.S. (1994): The method of cyclic projections for closed convex sets in Hilbert space. In: Censor, Y., Reich, S., eds., Optimization and Nonlinear Analysis, volume 204 of Contemporary Mathematics, pp. 1-38. American Mathematical Society, 1997. Proceedings on the Special Session on Optimization and Nonlinear Analysis, Jerusalem, May 1995
6. Bauschke, H.H., Borwein, J.M., Tseng, P. (1998): Metric regularity, strong chip, and chip are distinct properties. Preprint
7. Burke, J.V., Tseng, P. (1996): A unified analysis of Hoffman's bound via Fenchel duality. SIAM J. Optim. 6, 265-282
8. Chui, C.K., Deutsch, F., Ward, J.D. (1990): Constrained best approximation in Hilbert space. Constr. Approx. 6, 35-64
9. Chui, C.K., Deutsch, F., Ward, J.D. (1992): Constrained best approximation in Hilbert space, II. J. Approx. Theory 71, 213-238
10. Deutsch, F. (1995): The angle between subspaces of a Hilbert space. In: Singh, S.P., ed., Approximation Theory, Wavelets and Applications, pp. 107-130. Kluwer Academic Publishers
11. Deutsch, F. (1995): Interpolation from a convex subset of Hilbert space: a survey of some recent results. In: Singh, S.P., ed., Approximation Theory, Wavelets and Applications, pp. 95-105. Kluwer Academic Publishers
12. Deutsch, F. (1998): The role of the strong conical hull intersection property in convex optimization and approximation. In: Chui, C.K., Schumaker, L.L., eds., Approximation Theory IX, Vanderbilt University Press, Nashville, TN
13. Deutsch, F., Li, W., Swetits, J. (1997): Fenchel duality and the strong conical hull intersection property. J. Optim. Theory Appl. To appear
14. Deutsch, F., Li, W., Ward, J.D. (1998): Best approximation from the intersection of finitely many closed convex subsets in Hilbert space, weak Slater conditions, and the strong conical hull intersection property. To appear in SIAM J. Optim.
15. Deutsch, F., Li, W., Ward, J.D. (1997): A dual approach to constrained interpolation from a convex subset of Hilbert space. J. Approx. Theory 90, 385-414
16. Deutsch, F., Ubhaya, V.A., Ward, J.D., Xu, Y. (1996): Constrained best approximation in Hilbert space III. Applications to n-convex functions. Constructive Approx. 12, 361-384
17. Friedrichs, K. (1937): On certain inequalities and characteristic value problems for analytic functions and for functions of two variables. Trans. Am. Math. Soc. 41, 321-364
18. Hiriart-Urruty, J.-B., Lemaréchal, C. (1993): Convex Analysis and Minimization Algorithms I, volume 305 of Grundlehren der mathematischen Wissenschaften. Springer
19. Hiriart-Urruty, J.-B., Lemaréchal, C. (1993): Convex Analysis and Minimization Algorithms II, volume 306 of Grundlehren der mathematischen Wissenschaften. Springer
20. Hoffman, A.J. (1952): On approximate solutions of systems of linear inequalities. J. Res. Nat. Bur. Stand. 49, 263-265
21. Holmes, R.B. (1975): Geometric Functional Analysis and its Applications. Springer, New York
22. Jameson, G.J.O. (1972): The duality of pairs of wedges. Proc. Lond. Math. Soc. 24, 531-547
23. Jameson, G.J.O. (1974): Topology and Normed Spaces. Chapman and Hall
24. Kiwiel, K.C., Łopuch, B. (1997): Surrogate projection methods for finding fixed points of firmly nonexpansive mappings. SIAM J. Optim. 7, 1084-1102
25. Klatte, D., Li, W. (1999): Asymptotic constraint qualifications and global error bounds for convex inequalities. Math. Program. 84, 137-160
26. Lewis, A.S., Pang, J.-S. (1997): Error bounds for convex inequality systems. In: Crouzeix, J.-P., ed., Generalized Convexity, pp. 75-110. Proceedings of the Fifth Symposium on Generalized Convexity, Luminy-Marseille
27. Li, W. (1997): Abadie's constraint qualification, metric regularity, and error bounds for differentiable convex inequalities. SIAM J. Optim. 7, 966-978
28. Mangasarian, O.L. (1985): A condition number for differentiable convex inequalities. Math. Oper. Res. 10, 175-179
29. Pang, J.-S. (1997): Error bounds in mathematical programming. Math. Program. 79, 299-332
30. Robinson, S.M. (1975): An application of error bounds for convex programming in a linear space. SIAM J. Control 13, 271-273
31. Robinson, S.M. (1976): Regularity and stability for convex multivalued functions. Math. Oper. Res. 1, 130-143
32. Rockafellar, R.T. (1970): Convex Analysis. Princeton University Press, Princeton, NJ
33. Rockafellar, R.T., Wets, R.J.-B. (1998): Variational Analysis, volume 317 of Grundlehren der mathematischen Wissenschaften. Springer
34. Valentine, F.A. (1964): Convex Sets. McGraw-Hill
35. Wilansky, A. (1964): Functional Analysis. Blaisdell Publishing Company