메뉴 건너뛰기




Volumn 335, Issue 1, 2007, Pages 168-183

Uniformity and inexact version of a proximal method for metrically regular mappings

Author keywords

Metric regularity; Proximal point algorithm; Set valued mapping; Strong regularity; Strong subregularity

Indexed keywords


EID: 34347336607     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.01.050     Document Type: Article
Times cited : (12)

References (26)
  • 1
    • 34347356122 scopus 로고    scopus 로고
    • F.J. Aragón Artacho, A.L. Dontchev, M.H. Geoffroy, Convergence of the proximal point method for metrically regular mappings, in press
  • 3
    • 0000410841 scopus 로고
    • An inverse mapping theorem for set-valued maps
    • Dontchev A.L., and Hager W.W. An inverse mapping theorem for set-valued maps. Proc. Amer. Math. Soc. 121 2 (1994) 481-489
    • (1994) Proc. Amer. Math. Soc. , vol.121 , Issue.2 , pp. 481-489
    • Dontchev, A.L.1    Hager, W.W.2
  • 4
    • 0001866786 scopus 로고
    • Characterizations of Lipschitz stability in optimization
    • Recent Developments in Well-posed Variational Problems. Lucchetti R., and Revalski J. (Eds), Kluwer Academic, Dordrecht
    • Dontchev A.L. Characterizations of Lipschitz stability in optimization. In: Lucchetti R., and Revalski J. (Eds). Recent Developments in Well-posed Variational Problems. Math. Appl. vol. 331 (1995), Kluwer Academic, Dordrecht 95-115
    • (1995) Math. Appl. , vol.331 , pp. 95-115
    • Dontchev, A.L.1
  • 5
    • 18844385553 scopus 로고    scopus 로고
    • Uniform convergence of the Newton method for Aubin continuous maps
    • Dontchev A.L. Uniform convergence of the Newton method for Aubin continuous maps. Serdica Math. J. 22 (1996) 385-398
    • (1996) Serdica Math. J. , vol.22 , pp. 385-398
    • Dontchev, A.L.1
  • 6
    • 0030521635 scopus 로고    scopus 로고
    • Characterization of strong regularity of variational inequalities over polyhedral convex sets
    • Dontchev A.L., and Rockafellar R.T. Characterization of strong regularity of variational inequalities over polyhedral convex sets. SIAM J. Control Optim. 6 (1996) 1087-1105
    • (1996) SIAM J. Control Optim. , vol.6 , pp. 1087-1105
    • Dontchev, A.L.1    Rockafellar, R.T.2
  • 8
    • 3943050689 scopus 로고    scopus 로고
    • Regularity and conditioning of solution mappings in variational analysis
    • Dontchev A.L., and Rockafellar R.T. Regularity and conditioning of solution mappings in variational analysis. Set-Valued Anal. 12 (2004) 79-109
    • (2004) Set-Valued Anal. , vol.12 , pp. 79-109
    • Dontchev, A.L.1    Rockafellar, R.T.2
  • 9
    • 17344362566 scopus 로고    scopus 로고
    • Inexact proximal point algorithms and descent methods in optimization
    • Humes C., and Silva P. Inexact proximal point algorithms and descent methods in optimization. Optim. Eng. 6 2 (2005) 257-271
    • (2005) Optim. Eng. , vol.6 , Issue.2 , pp. 257-271
    • Humes, C.1    Silva, P.2
  • 10
    • 0000841855 scopus 로고    scopus 로고
    • Metric regularity and subdifferential calculus
    • English translation in:
    • Ioffe A.D. Metric regularity and subdifferential calculus. Uspekhi Mat. Nauk 55 3 (2000) 103-162 English translation in:
    • (2000) Uspekhi Mat. Nauk , vol.55 , Issue.3 , pp. 103-162
    • Ioffe, A.D.1
  • 11
    • 0034361329 scopus 로고    scopus 로고
    • Metric regularity and subdifferential calculus
    • Ioffe A.D. Metric regularity and subdifferential calculus. Russian Math. Surveys 55 (2000) 501-558
    • (2000) Russian Math. Surveys , vol.55 , pp. 501-558
    • Ioffe, A.D.1
  • 12
    • 0242679720 scopus 로고    scopus 로고
    • Inexact variants of the proximal point algorithm without monotonicity
    • Iusem A.N., Pennanen T., and Svaiter B.F. Inexact variants of the proximal point algorithm without monotonicity. SIAM J. Optim. 13 (2003) 1080-1097
    • (2003) SIAM J. Optim. , vol.13 , pp. 1080-1097
    • Iusem, A.N.1    Pennanen, T.2    Svaiter, B.F.3
  • 13
    • 0005382209 scopus 로고
    • Semi-continuity of set-valued monotone mappings
    • Kenderov P. Semi-continuity of set-valued monotone mappings. Fund. Math. 88 (1975) 61-69
    • (1975) Fund. Math. , vol.88 , pp. 61-69
    • Kenderov, P.1
  • 14
    • 24944447156 scopus 로고    scopus 로고
    • Convergence of generalized proximal point algorithms
    • Marino G., and Xu H.-K. Convergence of generalized proximal point algorithms. Commun. Pure Appl. Anal. 3 4 (2004) 791-808
    • (2004) Commun. Pure Appl. Anal. , vol.3 , Issue.4 , pp. 791-808
    • Marino, G.1    Xu, H.-K.2
  • 15
    • 0001566816 scopus 로고
    • Régularisation d'inéquations variationnelles par approximations successives
    • Martinet B. Régularisation d'inéquations variationnelles par approximations successives. Rev. Fr. Inform. Rech. Opér. 3 (1970) 154-158
    • (1970) Rev. Fr. Inform. Rech. Opér. , vol.3 , pp. 154-158
    • Martinet, B.1
  • 16
    • 84966250815 scopus 로고
    • Complete characterization of openness, metric regularity, and Lipschitzian properties of multifunctions
    • Mordukhovich B.S. Complete characterization of openness, metric regularity, and Lipschitzian properties of multifunctions. Trans. Amer. Math. Soc. 340 1 (1993) 1-35
    • (1993) Trans. Amer. Math. Soc. , vol.340 , Issue.1 , pp. 1-35
    • Mordukhovich, B.S.1
  • 17
    • 34249303170 scopus 로고    scopus 로고
    • Variational Analysis and Generalized Differentiation I: Basic Theory
    • Springer-Verlag, Berlin
    • Mordukhovich B.S. Variational Analysis and Generalized Differentiation I: Basic Theory. Grundlehren Math. Wiss. vol. 330 (2006), Springer-Verlag, Berlin
    • (2006) Grundlehren Math. Wiss. , vol.330
    • Mordukhovich, B.S.1
  • 18
    • 0036473820 scopus 로고    scopus 로고
    • Local convergence of the proximal point algorithm and multiplier methods without monotonicity
    • Pennanen T. Local convergence of the proximal point algorithm and multiplier methods without monotonicity. Math. Oper. Res. 27 (2002) 170-191
    • (2002) Math. Oper. Res. , vol.27 , pp. 170-191
    • Pennanen, T.1
  • 19
    • 0016952838 scopus 로고
    • Regularity and stability for convex multivalued functions
    • Robinson S.M. Regularity and stability for convex multivalued functions. Math. Oper. Res. 1 2 (1976) 130-143
    • (1976) Math. Oper. Res. , vol.1 , Issue.2 , pp. 130-143
    • Robinson, S.M.1
  • 20
    • 0001052352 scopus 로고
    • Some continuity properties of polyhedral multifunctions
    • Robinson S.M. Some continuity properties of polyhedral multifunctions. Math. Program. Study 14 (1981) 206-214
    • (1981) Math. Program. Study , vol.14 , pp. 206-214
    • Robinson, S.M.1
  • 21
    • 0016985417 scopus 로고
    • Monotone operators and the proximal point algorithm
    • Rockafellar R.T. Monotone operators and the proximal point algorithm. SIAM J. Control Optim. 14 (1976) 877-898
    • (1976) SIAM J. Control Optim. , vol.14 , pp. 877-898
    • Rockafellar, R.T.1
  • 23
    • 22844456506 scopus 로고    scopus 로고
    • A hybrid projection-proximal point algorithm
    • Solodov M.V., and Svaiter B.F. A hybrid projection-proximal point algorithm. J. Convex Anal. 6 1 (1999) 59-70
    • (1999) J. Convex Anal. , vol.6 , Issue.1 , pp. 59-70
    • Solodov, M.V.1    Svaiter, B.F.2
  • 24
    • 0035518990 scopus 로고    scopus 로고
    • A unified framework for some inexact proximal point algorithms
    • Solodov M.V., and Svaiter B.F. A unified framework for some inexact proximal point algorithms. Numer. Funct. Anal. Optim. 22 7-8 (2001) 1013-1035
    • (2001) Numer. Funct. Anal. Optim. , vol.22 , Issue.7-8 , pp. 1013-1035
    • Solodov, M.V.1    Svaiter, B.F.2
  • 25
    • 0001012728 scopus 로고
    • Multifunctions with convex closed graph
    • Ursescu C. Multifunctions with convex closed graph. Czechoslovak Math. J. 25(100) 3 (1975) 438-441
    • (1975) Czechoslovak Math. J. , vol.25 100 , Issue.3 , pp. 438-441
    • Ursescu, C.1
  • 26
    • 15244361360 scopus 로고    scopus 로고
    • A relaxed approximate proximal point algorithm
    • Yang Z., and He B. A relaxed approximate proximal point algorithm. Ann. Oper. Res. 133 (2005) 119-125
    • (2005) Ann. Oper. Res. , vol.133 , pp. 119-125
    • Yang, Z.1    He, B.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.