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Volumn 133, Issue 6, 2005, Pages 1829-1835

A new proximal point iteration that converges weakly but not in norm

Author keywords

Proximal point algorithm; Support point; Weak convergence

Indexed keywords


EID: 20144368670     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-05-07719-1     Document Type: Conference Paper
Times cited : (35)

References (17)
  • 1
    • 0003851536 scopus 로고    scopus 로고
    • Ph.D. Thesis, Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, August
    • H. H. Bauschke, Projection Algorithms and Monotone Operators, Ph.D. Thesis, Department of Mathematics and Statistics, Simon Fraser University, Burnaby, British Columbia, August 1996. Available at http://www.cecm.sfu.ca/ preprints/1996pp.html.
    • (1996) Projection Algorithms and Monotone Operators
    • Bauschke, H.H.1
  • 2
    • 0030246542 scopus 로고    scopus 로고
    • On projection algorithms for solving convex feasibility problems
    • MR1409591 (98f:90045)
    • H. H. Bauschke and J. M. Borwein, On projection algorithms for solving convex feasibility problems, SIAM Rev., 38 (1996), 367-426. MR1409591 (98f:90045)
    • (1996) SIAM Rev. , vol.38 , pp. 367-426
    • Bauschke, H.H.1    Borwein, J.M.2
  • 3
    • 0001448913 scopus 로고
    • On the Convergence of the von Neumann's Alternating Projection Algorithm for Two Sets
    • MR1239403 (95d:65048)
    • H. H. Bauschke and J. M. Borwein, On the Convergence of the von Neumann's Alternating Projection Algorithm for Two Sets, Set-Valued Anal., 1 (1993), 185-212. MR1239403 (95d:65048)
    • (1993) Set-Valued Anal. , vol.1 , pp. 185-212
    • Bauschke, H.H.1    Borwein, J.M.2
  • 4
    • 0035351666 scopus 로고    scopus 로고
    • A weak-to-strong convergence principle for Fejérmonotone methods in Hubert spaces
    • MR1895827 (2003f:65101)
    • H. H. Bauschke and P. L. Combettes, A weak-to-strong convergence principle for Fejérmonotone methods in Hubert spaces, Math. Oper. Res., 26 (2001), 248-264. MR1895827 (2003f:65101)
    • (2001) Math. Oper. Res. , vol.26 , pp. 248-264
    • Bauschke, H.H.1    Combettes, P.L.2
  • 5
    • 0347269125 scopus 로고    scopus 로고
    • Projection and proximal point methods: Convergence results and counterexamples
    • MR2036787 (2004m:47116)
    • H. H. Bauschke, E. Matoušková, and S. Reich, Projection and proximal point methods: convergence results and counterexamples, Nonlinear Anal., 56 (2004), 715-738. MR2036787 (2004m:47116)
    • (2004) Nonlinear Anal. , vol.56 , pp. 715-738
    • Bauschke, H.H.1    Matoušková, E.2    Reich, S.3
  • 6
    • 0001336448 scopus 로고
    • The method of successive projection for finding a common point of convex sets
    • L. M. Bregman, The method of successive projection for finding a common point of convex sets, Soviet Math. Dokl., 6 (1965), 688-692.
    • (1965) Soviet Math. Dokl. , vol.6 , pp. 688-692
    • Bregman, L.M.1
  • 7
    • 51249180487 scopus 로고
    • Produits infinis de résolvantes
    • MR0491922 (80b:47068)
    • H. Brézis and P.-L. Lions, Produits infinis de résolvantes, Israel J. Math., 29 (1978), 329-345. MR0491922 (80b:47068)
    • (1978) Israel J. Math. , vol.29 , pp. 329-345
    • Brézis, H.1    Lions, P.-L.2
  • 9
    • 0026123473 scopus 로고
    • On the convergence of the proximal point algorithm for convex minimization
    • MR1092735 (92c:90086)
    • O. Güler, On the convergence of the proximal point algorithm for convex minimization, SIAM J. Control Optim., 29 (1991), 403-419. MR1092735 (92c:90086)
    • (1991) SIAM J. Control Optim. , vol.29 , pp. 403-419
    • Güler, O.1
  • 10
    • 2042504393 scopus 로고    scopus 로고
    • An alternating projection that does not converge in norm
    • MR2055986 (2005a:47093)
    • H. Hundal, An Alternating Projection that Does Not Converge in Norm, Nonlinear Anal., 57 (2004), 35-61. MR2055986 (2005a:47093)
    • (2004) Nonlinear Anal. , vol.57 , pp. 35-61
    • Hundal, H.1
  • 11
    • 0001566816 scopus 로고
    • Régularisation d'inéquations variationnelles par approximations successives
    • MR0298899 (45:7948)
    • B. Martinet, Régularisation d'inéquations variationnelles par approximations successives, Rev. Française Informat. Recherche Opérationnelle (Ser. R-3), 4 (1970), 154-158. MR0298899 (45:7948)
    • (1970) Rev. Française Informat. Recherche Opérationnelle (Ser. R-3) , vol.4 , pp. 154-158
    • Martinet, B.1
  • 12
    • 84972488065 scopus 로고
    • Monotone (nonlinear) operators in a Hubert space
    • MR0169064 (29:6319)
    • G. Minty, Monotone (nonlinear) operators in a Hubert space, Duke Math. J., 29 (1962), 341-346. MR0169064 (29:6319)
    • (1962) Duke Math. J. , vol.29 , pp. 341-346
    • Minty, G.1
  • 13
    • 0000276924 scopus 로고
    • Proximité et dualité dans un espace hilbertien
    • MR0201952 (34:1829)
    • J.-J. Moreau, Proximité et dualité dans un espace hilbertien, Bull. Soc. Math. France, 93 (1965), 273-299. MR0201952 (34:1829)
    • (1965) Bull. Soc. Math. France , vol.93 , pp. 273-299
    • Moreau, J.-J.1
  • 15
    • 0016985417 scopus 로고
    • Monotone operators and the proximal point algorithm
    • MR0410483 (53:14232)
    • R. T. Rockafellar, Monotone operators and the proximal point algorithm, SIAM J. Control Optim., 14 (1976), 877-898. MR0410483 (53:14232)
    • (1976) SIAM J. Control Optim. , vol.14 , pp. 877-898
    • Rockafellar, R.T.1
  • 17
    • 0001279962 scopus 로고    scopus 로고
    • Forcing strong convergence of proximal point iterations in a Hubert space
    • MR1734665 (2000j:90077)
    • M. V. Solodov and B. F. Svaiter, Forcing strong convergence of proximal point iterations in a Hubert space, Math. Program. (Ser. A), 87 (2000), 189-202. MR1734665 (2000j:90077)
    • (2000) Math. Program. (Ser. A) , vol.87 , pp. 189-202
    • Solodov, M.V.1    Svaiter, B.F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.