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Volumn 29, Issue 9-10, 2008, Pages 987-1033

Mann-type steepest-descent and modified hybrid steepest-descent methods for variational inequalities in banach spaces

Author keywords

Convergence analysis; Mann type steepest descent method; Modified hybrid steepest descent method; Nonexpansive maps; Resolvent operators; Variational inequalities

Indexed keywords

ALGORITHMS; BANACH SPACES; CONVERGENCE OF NUMERICAL METHODS; OPTIMAL CONTROL SYSTEMS; SOLUTIONS; TOPOLOGY; TREES (MATHEMATICS); VARIATIONAL TECHNIQUES;

EID: 56349116819     PISSN: 01630563     EISSN: 15322467     Source Type: Journal    
DOI: 10.1080/01630560802418391     Document Type: Article
Times cited : (82)

References (45)
  • 1
    • 0001884161 scopus 로고    scopus 로고
    • Metric and generalized projection operators in Banach spaces: Properties and applications
    • Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, A. G. Kartsatos, ed, Marcel Dekker, New York, pp
    • Y.I. Alber (1996). Metric and generalized projection operators in Banach spaces: Properties and applications. In: Theory and Applications of Nonlinear Operators of Accretive and Monotone Type. (A. G. Kartsatos, ed.). Lecture Notes in Pure and Applied Mathematics, Vol. 178. Marcel Dekker, New York, pp. 15-50.
    • (1996) Lecture Notes in Pure and Applied Mathematics , vol.178 , pp. 15-50
    • Alber, Y.I.1
  • 2
    • 33749568335 scopus 로고    scopus 로고
    • Weak convergence of an iterative sequence for accretive operators in Banach spaces
    • Art. no. 35390
    • K. Aoyama, H. Iiduka, and W. Takahashi (2006). Weak convergence of an iterative sequence for accretive operators in Banach spaces. Fixed Point Theory Appl. 2006, Art. no. 35390.
    • (2006) Fixed Point Theory Appl , pp. 2006
    • Aoyama, K.1    Iiduka, H.2    Takahashi, W.3
  • 3
    • 56349114422 scopus 로고    scopus 로고
    • Strong convergence of Halpern's sequence for accretive operators in a Banach space
    • K. Aoyama, H. Iiduka, and W. Takahashi (2006). Strong convergence of Halpern's sequence for accretive operators in a Banach space. Panamer. Math. J. 16:97-104.
    • (2006) Panamer. Math. J , vol.16 , pp. 97-104
    • Aoyama, K.1    Iiduka, H.2    Takahashi, W.3
  • 4
    • 0000887243 scopus 로고
    • Convergence theorems for sequences of nonlinear operators in Banach spaces
    • F.E. Browder (1967). Convergence theorems for sequences of nonlinear operators in Banach spaces. Math. Z. 100:201-225.
    • (1967) Math. Z , vol.100 , pp. 201-225
    • Browder, F.E.1
  • 5
    • 0000827660 scopus 로고
    • Construction of fixed points of nonlinear mappings in Hilbert space
    • F.E. Browder and W.V. Petryshyn (1967). Construction of fixed points of nonlinear mappings in Hilbert space. J. Math. Anal. Appl. 20:197-228.
    • (1967) J. Math. Anal. Appl , vol.20 , pp. 197-228
    • Browder, F.E.1    Petryshyn, W.V.2
  • 6
    • 1342265919 scopus 로고    scopus 로고
    • A unified treatment of some iterative algorithms in signal processing and image reconstruction
    • C. Byrne (2004). A unified treatment of some iterative algorithms in signal processing and image reconstruction. Inverse Problems 20:103-120.
    • (2004) Inverse Problems , vol.20 , pp. 103-120
    • Byrne, C.1
  • 7
    • 34249819673 scopus 로고    scopus 로고
    • An extragradient-like approximation method for variational inequality problems and fixed point problems
    • L.C. Ceng and J.C. Yao (2007). An extragradient-like approximation method for variational inequality problems and fixed point problems. Appl. Math. Comput. 190:205-215.
    • (2007) Appl. Math. Comput , vol.190 , pp. 205-215
    • Ceng, L.C.1    Yao, J.C.2
  • 9
    • 0001399612 scopus 로고
    • Zero of accretive operators
    • K. Deimling (1974). Zero of accretive operators. Manuscripta Math. 13:365-374.
    • (1974) Manuscripta Math , vol.13 , pp. 365-374
    • Deimling, K.1
  • 10
    • 0031999680 scopus 로고    scopus 로고
    • Minimizing certain convex functions over the intersection of the fixed-point sets of nonexpansive mappings
    • F. Deutsch and I. Yamada (1998). Minimizing certain convex functions over the intersection of the fixed-point sets of nonexpansive mappings. Numer. Funct. Anal. Optim. 19:33-56.
    • (1998) Numer. Funct. Anal. Optim , vol.19 , pp. 33-56
    • Deutsch, F.1    Yamada, I.2
  • 13
    • 84972584068 scopus 로고
    • Some geometric properties related to the fixed point theory for nonexpansive mappings
    • J.P. Gossez and E. Lami Dozo (1972). Some geometric properties related to the fixed point theory for nonexpansive mappings. Pacific J. Math. 40:565-573.
    • (1972) Pacific J. Math , vol.40 , pp. 565-573
    • Gossez, J.P.1    Lami Dozo, E.2
  • 14
    • 0026123473 scopus 로고
    • On the convergence of the proximal point algorithm for convex optimization
    • O. Güler (1991). On the convergence of the proximal point algorithm for convex optimization. SIAM J. Control Optim. 29:403-419.
    • (1991) SIAM J. Control Optim , vol.29 , pp. 403-419
    • Güler, O.1
  • 15
    • 42949168170 scopus 로고    scopus 로고
    • Strong convergence studied by a hybrid type method for monotone operators in a Banach space
    • H. Iiduka and W. Takahashi (2008). Strong convergence studied by a hybrid type method for monotone operators in a Banach space. Nonlinear Anal. 68:3679-3688.
    • (2008) Nonlinear Anal , vol.68 , pp. 3679-3688
    • Iiduka, H.1    Takahashi, W.2
  • 16
    • 35248835038 scopus 로고    scopus 로고
    • Weak convergence of a projection algorithm for variational inequalities in a Banach space
    • H. Iiduka and W. Takahashi (2008). Weak convergence of a projection algorithm for variational inequalities in a Banach space. J. Math. Anal. Appl. 339:668-679.
    • (2008) J. Math. Anal. Appl , vol.339 , pp. 668-679
    • Iiduka, H.1    Takahashi, W.2
  • 17
    • 0000743842 scopus 로고
    • Variational inequalities and the pricing of American options
    • P. Jaillet, D. Lamberton, and B. Lapeyre (1990). Variational inequalities and the pricing of American options. Acta Appl. Math. 21:263-289.
    • (1990) Acta Appl. Math , vol.21 , pp. 263-289
    • Jaillet, P.1    Lamberton, D.2    Lapeyre, B.3
  • 18
    • 10644249739 scopus 로고    scopus 로고
    • Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces
    • J.S. Jung (2005). Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces. J. Math. Anal. Appl. 302:509-520.
    • (2005) J. Math. Anal. Appl , vol.302 , pp. 509-520
    • Jung, J.S.1
  • 19
    • 0032140764 scopus 로고    scopus 로고
    • Strong convergence theorems for nonexpansive nonself-mappings in Banach spaces
    • J.S. Jung and S.S. Kim (1998). Strong convergence theorems for nonexpansive nonself-mappings in Banach spaces. Nonlinear Anal. 33:321-329.
    • (1998) Nonlinear Anal , vol.33 , pp. 321-329
    • Jung, J.S.1    Kim, S.S.2
  • 20
    • 14544304518 scopus 로고    scopus 로고
    • Strong convergence of modified Mann iterations
    • T.H. Kim and H.K. Xu (2005). Strong convergence of modified Mann iterations. Nonlinear Anal. 61:51-60.
    • (2005) Nonlinear Anal , vol.61 , pp. 51-60
    • Kim, T.H.1    Xu, H.K.2
  • 23
    • 0000222831 scopus 로고
    • Fixed point theorems for asymptotically nonexpansive mappings
    • T.C. Lim and H.K. Xu (1994). Fixed point theorems for asymptotically nonexpansive mappings. Nonlinear Anal. 22:1345-1355.
    • (1994) Nonlinear Anal , vol.22 , pp. 1345-1355
    • Lim, T.C.1    Xu, H.K.2
  • 24
    • 0000736340 scopus 로고
    • Approximation de points fixes de contractions
    • P.L. Lions (1977). Approximation de points fixes de contractions. C. R. Math. Acad. Sci. Paris. 284:1357-1359.
    • (1977) C. R. Math. Acad. Sci. Paris , vol.284 , pp. 1357-1359
    • Lions, P.L.1
  • 25
    • 84968518052 scopus 로고
    • Mean value methods in iteration
    • W.R. Mann (1953). Mean value methods in iteration. Proc. Am. Math. Soc. 4:506-510.
    • (1953) Proc. Am. Math. Soc , vol.4 , pp. 506-510
    • Mann, W.R.1
  • 26
    • 33846303213 scopus 로고    scopus 로고
    • Weak and strong convergence theorems for strict pseudocontractions in Hilbert spaces
    • G. Marino and H.K. Xu (2007). Weak and strong convergence theorems for strict pseudocontractions in Hilbert spaces. J. Math. Anal. Appl. 329:336-346.
    • (2007) J. Math. Anal. Appl , vol.329 , pp. 336-346
    • Marino, G.1    Xu, H.K.2
  • 27
    • 33746027163 scopus 로고
    • Differential equations on closed subsets of a Banach space
    • R.H. Martin (1973). Differential equations on closed subsets of a Banach space. Trans. Am. Math. Soc. 179:399-414.
    • (1973) Trans. Am. Math. Soc , vol.179 , pp. 399-414
    • Martin, R.H.1
  • 29
    • 0037845289 scopus 로고    scopus 로고
    • Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups
    • K. Nakajo and W. Takahashi (2003). Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups. J. Math. Anal. Appl. 279:372-379.
    • (2003) J. Math. Anal. Appl , vol.279 , pp. 372-379
    • Nakajo, K.1    Takahashi, W.2
  • 31
    • 33846332774 scopus 로고    scopus 로고
    • Approximation of a zero point of accretive operator in Banach spaces
    • X.L. Qin and Y.F. Su (2007). Approximation of a zero point of accretive operator in Banach spaces. J. Math. Anal. Appl. 329:415-424.
    • (2007) J. Math. Anal. Appl , vol.329 , pp. 415-424
    • Qin, X.L.1    Su, Y.F.2
  • 32
    • 0001720708 scopus 로고
    • Weak convergence theorems for nonexpansive mappings in Banach spaces
    • S. Reich (1979). Weak convergence theorems for nonexpansive mappings in Banach spaces. J. Math. Anal. Appl. 67:274-276.
    • (1979) J. Math. Anal. Appl , vol.67 , pp. 274-276
    • Reich, S.1
  • 33
    • 0000928424 scopus 로고
    • Product formulas, nonlinear semigroups and accretive operators
    • S. Reich (1980). Product formulas, nonlinear semigroups and accretive operators. J. Funct. Anal. 36:147-168.
    • (1980) J. Funct. Anal , vol.36 , pp. 147-168
    • Reich, S.1
  • 34
    • 33646371944 scopus 로고    scopus 로고
    • Viscosity approximation methods for nonexpansive nonselfmappings
    • Y.S. Song and R.D. Chen (2006). Viscosity approximation methods for nonexpansive nonselfmappings, J. Math. Anal. Appl. 321:316-326.
    • (2006) J. Math. Anal. Appl , vol.321 , pp. 316-326
    • Song, Y.S.1    Chen, R.D.2
  • 35
    • 34047253218 scopus 로고    scopus 로고
    • Convergence theorems of iterative algorithms for continuous pseudocontractive mappings
    • Y.S. Song and R.D. Chen (2007). Convergence theorems of iterative algorithms for continuous pseudocontractive mappings. Nonlinear Anal. 67(2):486-497.
    • (2007) Nonlinear Anal , vol.67 , Issue.2 , pp. 486-497
    • Song, Y.S.1    Chen, R.D.2
  • 37
    • 0036692463 scopus 로고    scopus 로고
    • Iterative algorithms for nonlinear operators
    • H.K. Xu (2002). Iterative algorithms for nonlinear operators. J. London Math. Soc. 66(2): 240-256.
    • (2002) J. London Math. Soc , vol.66 , Issue.2 , pp. 240-256
    • Xu, H.K.1
  • 38
    • 4544256112 scopus 로고    scopus 로고
    • Viscosity approximation methods for nonexpansive mappings
    • H.K. Xu (2004). Viscosity approximation methods for nonexpansive mappings. J. Math. Anal. Appl. 298:279-291.
    • (2004) J. Math. Anal. Appl , vol.298 , pp. 279-291
    • Xu, H.K.1
  • 39
    • 29144521943 scopus 로고    scopus 로고
    • Strong convergence of an iterative method for nonexpansive and accretive operators
    • H.K. Xu (2006). Strong convergence of an iterative method for nonexpansive and accretive operators. J. Math. Anal. Appl. 314:631-643.
    • (2006) J. Math. Anal. Appl , vol.314 , pp. 631-643
    • Xu, H.K.1
  • 40
    • 0344512422 scopus 로고    scopus 로고
    • Convergence of hybrid steepest-descent methods for variational inequalities
    • H.K. Xu and T.H. Kim (2003). Convergence of hybrid steepest-descent methods for variational inequalities. J. Optim. Theory Appl. 119:185-201.
    • (2003) J. Optim. Theory Appl , vol.119 , pp. 185-201
    • Xu, H.K.1    Kim, T.H.2
  • 41
    • 77956693893 scopus 로고    scopus 로고
    • The hybrid steepest descent method for the variational inequality problem over the intersection of fixed-point sets of nonexpansive mappings
    • D. Butnariu, Y. Censor, and S. Reich, eds, Elsevier, New York, pp
    • I. Yamada (2001). The hybrid steepest descent method for the variational inequality problem over the intersection of fixed-point sets of nonexpansive mappings. In: Inherently Parallel Algorithms for Feasibility and Optimization and Their Applications. (D. Butnariu, Y. Censor, and S. Reich, eds.). Elsevier, New York, pp. 473-504.
    • (2001) Inherently Parallel Algorithms for Feasibility and Optimization and Their Applications , pp. 473-504
    • Yamada, I.1
  • 43
    • 33745821822 scopus 로고    scopus 로고
    • Ishikawa iteration with errors for approximating fixed points of strictly pseudocontractive mappings of Browder-Petryshyn type
    • L.C. Zeng, G.M. Lee, and N.C. Wong (2006). Ishikawa iteration with errors for approximating fixed points of strictly pseudocontractive mappings of Browder-Petryshyn type. Taiwanese J. Math. 10(1):87-99.
    • (2006) Taiwanese J. Math , vol.10 , Issue.1 , pp. 87-99
    • Zeng, L.C.1    Lee, G.M.2    Wong, N.C.3
  • 44
    • 29144447891 scopus 로고    scopus 로고
    • Convergence of hybrid steepest-descent methods for generalized variational inequalities
    • L.C. Zeng, N.C. Wong, and J.C. Yao (2006). Convergence of hybrid steepest-descent methods for generalized variational inequalities. Acta Math. Sin. (Engl. Ser.) 22(1):1-12.
    • (2006) Acta Math. Sin. (Engl. Ser.) , vol.22 , Issue.1 , pp. 1-12
    • Zeng, L.C.1    Wong, N.C.2    Yao, J.C.3
  • 45
    • 33847646305 scopus 로고    scopus 로고
    • Convergence analysis of modified hybrid steepestdescent methods with variable parameters for variational inequalities
    • L.C. Zeng, N.C. Wong, and J.C. Yao (2007). Convergence analysis of modified hybrid steepestdescent methods with variable parameters for variational inequalities, J. Optim. Theory Appl. 132:51-69.
    • (2007) J. Optim. Theory Appl , vol.132 , pp. 51-69
    • Zeng, L.C.1    Wong, N.C.2    Yao, J.C.3


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