메뉴 건너뛰기




Volumn 131, Issue 12, 2003, Pages 3757-3766

Construction of best Bregman approximations in reflexive Banach spaces

Author keywords

Best approximation; Bregman distance; Decomposition; Haugazeau

Indexed keywords


EID: 0345138997     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-03-07050-3     Document Type: Conference Paper
Times cited : (67)

References (25)
  • 1
    • 23044531274 scopus 로고    scopus 로고
    • Essential smoothness, essential strict convexity, and Legendre functions in Banach spaces
    • MR 2002k:49040
    • H. H. Bauschke, J. M. Borwein, and P. L. Combettes, Essential smoothness, essential strict convexity, and Legendre functions in Banach spaces, Comm. Contemp. Math., 3 (2001), 615-647. MR 2002k:49040
    • (2001) Comm. Contemp. Math. , vol.3 , pp. 615-647
    • Bauschke, H.H.1    Borwein, J.M.2    Combettes, P.L.3
  • 3
    • 0035351666 scopus 로고    scopus 로고
    • A weak-to-strong convergence principle for Fejér-monotone methods in Hilbert spaces
    • H. H. Bauschke and P. L. Combettes, A weak-to-strong convergence principle for Fejér-monotone methods in Hilbert spaces, Math. Oper. Res., 26 (2001), 248-264.
    • (2001) Math. Oper. Res. , vol.26 , pp. 248-264
    • Bauschke, H.H.1    Combettes, P.L.2
  • 4
    • 0042391294 scopus 로고    scopus 로고
    • Dykstra's algorithm with Bregman projections: A convergence proof
    • MR 2002e:90062
    • H. H. Bauschke and A. S. Lewis, Dykstra's algorithm with Bregman projections: A convergence proof, Optimization, 48 (2000), 409-427. MR 2002e:90062
    • (2000) Optimization , vol.48 , pp. 409-427
    • Bauschke, H.H.1    Lewis, A.S.2
  • 5
    • 0000172343 scopus 로고
    • On convex functions having points of Gâteaux differentiability which are not points of Fréchet differentiability
    • MR 941:46018
    • J. M. Borwein and M. Fabian, On convex functions having points of Gâteaux differentiability which are not points of Fréchet differentiability, Canad. J. Math., 45 (1993), 1121-1134. MR 941:46018
    • (1993) Canad. J. Math. , vol.45 , pp. 1121-1134
    • Borwein, J.M.1    Fabian, M.2
  • 6
    • 0002436271 scopus 로고
    • A method for finding projections onto the intersection of convex sets in Hilbert spaces
    • Springer-Verlag, New York, MR 87m:49024
    • J. P. Boyle and R. L. Dykstra, A method for finding projections onto the intersection of convex sets in Hilbert spaces, in Lecture Notes in Statistics, Vol. 37, Springer-Verlag, New York, 1986, 28-47. MR 87m:49024
    • (1986) Lecture Notes in Statistics , vol.37 , pp. 28-47
    • Boyle, J.P.1    Dykstra, R.L.2
  • 7
    • 22844453400 scopus 로고    scopus 로고
    • Dykstra's algorithm as the nonlinear extension of Bregman's optimization method
    • MR 2001e:90054
    • L. M. Bregman, Y. Censor, and S. Reich, Dykstra's algorithm as the nonlinear extension of Bregman's optimization method, J. Convex Anal., 6 (1999), 319-333. MR 2001e:90054
    • (1999) J. Convex Anal. , vol.6 , pp. 319-333
    • Bregman, L.M.1    Censor, Y.2    Reich, S.3
  • 10
    • 0042972614 scopus 로고    scopus 로고
    • On uniform convexity, total convexity and the convergence of the proximal point and outer Bregman projection algorithms in Banach spaces
    • to appear
    • D. Butnariu, A. Iusem, and C. Zǎlinescu, On uniform convexity, total convexity and the convergence of the proximal point and outer Bregman projection algorithms in Banach spaces, J. Convex Anal., to appear.
    • J. Convex Anal.
    • Butnariu, D.1    Iusem, A.2    Zǎlinescu, C.3
  • 11
    • 0042613100 scopus 로고    scopus 로고
    • The Dykstra algorithm with Bregman projections
    • MR 99e:90111
    • Y. Censor and S. Reich, The Dykstra algorithm with Bregman projections, Commun. Appl. Anal., 2 (1998), 407-419. MR 99e:90111
    • (1998) Commun. Appl. Anal. , vol.2 , pp. 407-419
    • Censor, Y.1    Reich, S.2
  • 13
    • 0033889575 scopus 로고    scopus 로고
    • Strong convergence of block-iterative outer approximation methods for convex optimization
    • MR 2001b:90064
    • P. L. Combettes, Strong convergence of block-iterative outer approximation methods for convex optimization, SIAM J. Control Optim., 38 (2000), 538-565. MR 2001b:90064
    • (2000) SIAM J. Control Optim. , vol.38 , pp. 538-565
    • Combettes, P.L.1
  • 17
    • 25944434983 scopus 로고    scopus 로고
    • A strongly convergent hybrid proximal point method in Banach spaces
    • (presented at the IV Brazilian Workshop on Continuous Optimization, Rio de Janeiro, July 15) reporting on a forthcoming paper with B. F. Svaiter
    • R. Gárciga-Otero, A strongly convergent hybrid proximal point method in Banach spaces, conference talk (presented at the IV Brazilian Workshop on Continuous Optimization, Rio de Janeiro, July 15, 2002) reporting on a forthcoming paper with B. F. Svaiter.
    • (2002) Conference Talk
    • Gárciga-Otero, R.1
  • 19
    • 84987937647 scopus 로고
    • Eclatement de contraintes en parallèle pour la minimisation d'une forme quadratique
    • Springer-Verlag, New York
    • G. Pierra, Eclatement de contraintes en parallèle pour la minimisation d'une forme quadratique, in Lecture Notes in Computer Science, Vol. 41, Springer-Verlag, New York, 1976, 200-218.
    • (1976) Lecture Notes in Computer Science , vol.41 , pp. 200-218
    • Pierra, G.1
  • 22
    • 0001279962 scopus 로고    scopus 로고
    • Forcing strong convergence of proximal point iterations in a Hilbert space
    • MR 2000j:90077
    • M. V. Solodov and B. F. Svaiter, Forcing strong convergence of proximal point iterations in a Hilbert space, Math. Programming A, 87 (2000), 189-202. MR 2000j:90077
    • (2000) Math. Programming A , vol.87 , pp. 189-202
    • Solodov, M.V.1    Svaiter, B.F.2
  • 24
    • 0000759513 scopus 로고
    • On uniformly convex functions
    • MR 85a:26018
    • C. Zǎlinescu, On uniformly convex functions, J. Math. Anal. Appl., 95 (1983), 344-374. MR 85a:26018
    • (1983) J. Math. Anal. Appl. , vol.95 , pp. 344-374
    • Zǎlinescu, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.