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Volumn 46, Issue 5, 2007, Pages 1683-1704

Asymptotic convergence analysis of a new class of proximal point methods

Author keywords

Degenerate optimization; Multiple minima; Proximal point; Self adaptive method

Indexed keywords

ACCEPTANCE CRITERIA; ASYMPTOTIC CONVERGENCE; CONVEX FUNCTION; DEGENERATE OPTIMIZATION; FINITE DIMENSIONAL; HILBERT SPACE SETTING; LOCAL CONVERGENCE; LOCAL ERROR BOUND; LOCAL LINEAR; MULTIPLE MINIMA; NEW CLASS; NON-LINEAR FUNCTIONS; PROXIMAL POINT; PROXIMAL POINT METHODS; REGULARIZATION PARAMETERS; SELF-ADAPTIVE; SELF-ADAPTIVE METHOD; SMOOTH FUNCTIONS; SOLUTION SETS; SUBDIFFERENTIAL;

EID: 52649108109     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/060666627     Document Type: Article
Times cited : (13)

References (30)
  • 1
    • 0034345443 scopus 로고    scopus 로고
    • Lagrangian duality and related multiplier methods for variational inequality problems
    • A. AUSLENDER AND M. TEBOULLE, Lagrangian duality and related multiplier methods for variational inequality problems, SIAM J. Optim., 10 (2000), pp. 1097-1115.
    • (2000) SIAM J. Optim , vol.10 , pp. 1097-1115
    • AUSLENDER, A.1    TEBOULLE, M.2
  • 2
    • 16244375249 scopus 로고    scopus 로고
    • Proximal methods for cohypomonotone operators
    • P. L. COMBETTES AND T. PENNANEN, Proximal methods for cohypomonotone operators, SIAM J. Control Optim., 43 (2004), pp. 731-742.
    • (2004) SIAM J. Control Optim , vol.43 , pp. 731-742
    • COMBETTES, P.L.1    PENNANEN, T.2
  • 3
    • 0001702688 scopus 로고
    • Nonlinear proximal point algorithms using Bregman functions, with applications to convex programming
    • J. ECKSTEIN, Nonlinear proximal point algorithms using Bregman functions, with applications to convex programming, Math. Oper. Res., 18 (1993), pp. 203-226.
    • (1993) Math. Oper. Res , vol.18 , pp. 203-226
    • ECKSTEIN, J.1
  • 4
    • 0000680340 scopus 로고    scopus 로고
    • Approximate iterations in Bregman-function-based proximal algorithms
    • J. ECKSTEIN, Approximate iterations in Bregman-function-based proximal algorithms, Math. Programming, 83 (1998), pp. 113-123.
    • (1998) Math. Programming , vol.83 , pp. 113-123
    • ECKSTEIN, J.1
  • 5
    • 13744251115 scopus 로고    scopus 로고
    • On the convergence of the Levenberg-Marquardt method without nonsingularity assumption
    • J. FAN AND Y. YUAN, On the convergence of the Levenberg-Marquardt method without nonsingularity assumption, Computing, 74 (2005), pp. 23-39.
    • (2005) Computing , vol.74 , pp. 23-39
    • FAN, J.1    YUAN, Y.2
  • 6
    • 0025431938 scopus 로고
    • A generalization of the proximal point algorithm
    • C. D. HA, A generalization of the proximal point algorithm, SIAM J. Control Optim., 28 (1990), pp. 503-512.
    • (1990) SIAM J. Control Optim , vol.28 , pp. 503-512
    • HA, C.D.1
  • 7
    • 38949178770 scopus 로고    scopus 로고
    • Self-adaptive inexact proximal point methods
    • to appear
    • W. W. HAGER AND H. ZHANG, Self-adaptive inexact proximal point methods, Comput. Optim. Appl., to appear.
    • Comput. Optim. Appl
    • HAGER, W.W.1    ZHANG, H.2
  • 8
    • 17344362566 scopus 로고    scopus 로고
    • Inexact proximal point algorithms and descent methods in optimization
    • C. HUMES AND P. SILVA, Inexact proximal point algorithms and descent methods in optimization, Optim. Eng., 6 (2005), pp. 257-271.
    • (2005) Optim. Eng , vol.6 , pp. 257-271
    • HUMES, C.1    SILVA, P.2
  • 9
    • 0000148237 scopus 로고
    • Entropy-like proximal methods in convex programming
    • A. IUSEM, B. SVAITER, AND M. TEBOULLE, Entropy-like proximal methods in convex programming, Math. Oper. Res., 19 (1994), pp. 790-814.
    • (1994) Math. Oper. Res , vol.19 , pp. 790-814
    • IUSEM, A.1    SVAITER, B.2    TEBOULLE, M.3
  • 10
    • 0242679720 scopus 로고    scopus 로고
    • Inexact variants of the proximal point algorithm without monotonicity
    • A. N. IUSEM, T. PENNANEN, AND B. F. SVAITER, Inexact variants of the proximal point algorithm without monotonicity, SIAM J. Optim., 13 (2003), pp. 1080-1097.
    • (2003) SIAM J. Optim , vol.13 , pp. 1080-1097
    • IUSEM, A.N.1    PENNANEN, T.2    SVAITER, B.F.3
  • 12
    • 0000422429 scopus 로고    scopus 로고
    • Proximal point methods and nonconvex optimization
    • A. KAPLAN AND R. TICHATSCHKE, Proximal point methods and nonconvex optimization, J. Global Optim., 13 (1998), pp. 389-406.
    • (1998) J. Global Optim , vol.13 , pp. 389-406
    • KAPLAN, A.1    TICHATSCHKE, R.2
  • 13
    • 3543109143 scopus 로고    scopus 로고
    • Regularized Newton methods for convex minimization problems with singular solutions
    • D. LI, M. FUKUSHIMA, L. QI, AND N. YAMASHITA, Regularized Newton methods for convex minimization problems with singular solutions, Comput. Optim. Appl., 28 (2004), pp. 131-147.
    • (2004) Comput. Optim. Appl , vol.28 , pp. 131-147
    • LI, D.1    FUKUSHIMA, M.2    QI, L.3    YAMASHITA, N.4
  • 14
    • 0001413137 scopus 로고
    • Asymptotic convergence analysis of the proximal point algorithm
    • F. J. LUQUE, Asymptotic convergence analysis of the proximal point algorithm, SIAM J. Control Optim., 22 (1984), pp. 277-293.
    • (1984) SIAM J. Control Optim , vol.22 , pp. 277-293
    • LUQUE, F.J.1
  • 15
    • 0001566816 scopus 로고
    • Régularisation d'inéquations variationnelles par approximations successives
    • B. MARTINET, Régularisation d'inéquations variationnelles par approximations successives, Rev. Française Informat. Recherche Opérationnelle, 4 (1970), pp. 154-158.
    • (1970) Rev. Française Informat. Recherche Opérationnelle , vol.4 , pp. 154-158
    • MARTINET, B.1
  • 16
    • 0001729611 scopus 로고
    • Determination approachée d'un point fixe d'une application pseudo-contractante
    • B. MARTINET, Determination approachée d'un point fixe d'une application pseudo-contractante, C. R. Acad. Sci. Paris Sér. A-B, 274 (1972), pp. 163-165.
    • (1972) C. R. Acad. Sci. Paris Sér. A-B , vol.274 , pp. 163-165
    • MARTINET, B.1
  • 18
    • 0000276924 scopus 로고
    • Proximité et dualité dans un espace hilbertien
    • J. MOREAU, Proximité et dualité dans un espace hilbertien, Bull. Soc. Math. Prance, 93 (1965), pp. 273-299.
    • (1965) Bull. Soc. Math. Prance , vol.93 , pp. 273-299
    • MOREAU, J.1
  • 19
    • 0036473820 scopus 로고    scopus 로고
    • Local convergence of the proximal point algorithm and multiplier methods without monotonicity
    • T. PENNANEN, Local convergence of the proximal point algorithm and multiplier methods without monotonicity, Math. Oper. Res., 27 (2002), pp. 170-191.
    • (2002) Math. Oper. Res , vol.27 , pp. 170-191
    • PENNANEN, T.1
  • 20
    • 0016950796 scopus 로고
    • Augmented Lagrangians and applications of the proximal point algorithm in convex programming
    • R. T. ROCKAFELLAR, Augmented Lagrangians and applications of the proximal point algorithm in convex programming, Math. Oper. Res., 2 (1976), pp. 97-116.
    • (1976) Math. Oper. Res , vol.2 , pp. 97-116
    • ROCKAFELLAR, R.T.1
  • 21
    • 0016985417 scopus 로고
    • Monotone operators and the proximal point algorithm
    • R. T. ROCKAFELLAR, Monotone operators and the proximal point algorithm, SIAM J. Control Optim., 14 (1976), pp. 877-898.
    • (1976) SIAM J. Control Optim , vol.14 , pp. 877-898
    • ROCKAFELLAR, R.T.1
  • 24
    • 0000586985 scopus 로고    scopus 로고
    • A hybrid extragradient-proximal point algorithm using the enlargement of a maximal monotone operator
    • M. V. SOLODOV AND B. F. SVAITER, A hybrid extragradient-proximal point algorithm using the enlargement of a maximal monotone operator, Set-Valued Anal., 7 (1999), pp. 323-345.
    • (1999) Set-Valued Anal , vol.7 , pp. 323-345
    • SOLODOV, M.V.1    SVAITER, B.F.2
  • 25
    • 22844456506 scopus 로고    scopus 로고
    • A hybrid projection-proximal point algorithm
    • M. V. SOLODOV AND B. F. SVAITER, A hybrid projection-proximal point algorithm, J. Convex Anal., 6 (1999), pp. 59-70.
    • (1999) J. Convex Anal , vol.6 , pp. 59-70
    • SOLODOV, M.V.1    SVAITER, B.F.2
  • 26
    • 0035518990 scopus 로고    scopus 로고
    • A unified framework for some inexact proximal point algorithms
    • M. V. SOLODOV AND B. F. SVAITER, A unified framework for some inexact proximal point algorithms, Numer. Funct. Anal. Optim., 22 (2001), pp. 1013-1035.
    • (2001) Numer. Funct. Anal. Optim , vol.22 , pp. 1013-1035
    • SOLODOV, M.V.1    SVAITER, B.F.2
  • 27
    • 0000157662 scopus 로고
    • Submonotone mappings and the proximal point algorithm
    • J. E. SPINGARN, Submonotone mappings and the proximal point algorithm, Numer. Funct. Anal. Optim., 4 (1981), pp. 123-150.
    • (1981) Numer. Funct. Anal. Optim , vol.4 , pp. 123-150
    • SPINGARN, J.E.1
  • 28
    • 0002621771 scopus 로고    scopus 로고
    • Error bounds and superlinear convergence analysis of some Newton-type methods in optimization
    • G. Di Pillo and F. Giannessi, eds, Kluwer Academic Publishers, Dordrecht, The Netherlands
    • P. TSENG, Error bounds and superlinear convergence analysis of some Newton-type methods in optimization, in Nonlinear Optimization and Related Topics, G. Di Pillo and F. Giannessi, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000, pp. 445-462.
    • (2000) Nonlinear Optimization and Related Topics , pp. 445-462
    • TSENG, P.1
  • 29
    • 0034353734 scopus 로고    scopus 로고
    • The proximal point algorithm with genuine superlinear convergence for the monotone complementarity problem
    • N. YAMASHITA AND M. FUKUSHIMA, The proximal point algorithm with genuine superlinear convergence for the monotone complementarity problem, SIAM J. Optim., 11 (2000), pp. 364-379.
    • (2000) SIAM J. Optim , vol.11 , pp. 364-379
    • YAMASHITA, N.1    FUKUSHIMA, M.2
  • 30
    • 0011662308 scopus 로고    scopus 로고
    • On the rate of convergence of the Levenberg-Marquardt method
    • Springer-Verlag, Vienna
    • N. YAMASHITA AND M. FUKUSHIMA, On the rate of convergence of the Levenberg-Marquardt method, in Topics in Numerical Analysis, Comput. Suppl. 15, Springer-Verlag, Vienna, 2001, pp. 239-249.
    • (2001) Topics in Numerical Analysis, Comput , Issue.SUPPL. 15 , pp. 239-249
    • YAMASHITA, N.1    FUKUSHIMA, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.