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Volumn 29, Issue 7-8, 2008, Pages 820-834

Extension of the hybrid steepest descent method to a class of variational inequalities and fixed point problems with nonself-mappings

Author keywords

Bilevel optimization; Convex minimization; Fixed point method; Variational inequality; Viscosity method

Indexed keywords

BILEVEL OPTIMIZATION; CONVERGENCE RESULTS; CONVEX MINIMIZATION; FIXE D POINTS; FIXED POINT METHOD; FIXED-POINT METHODS; HYBRID STEEPEST DESCENT METHOD; STRONG CONVERGENCE; TO MANY; VARIATIONAL INEQUALITIES; VARIATIONAL INEQUALITY; VISCOSITY METHOD;

EID: 52149108926     PISSN: 01630563     EISSN: 15322467     Source Type: Journal    
DOI: 10.1080/01630560802279371     Document Type: Article
Times cited : (17)

References (21)
  • 1
    • 0000827660 scopus 로고
    • Construction of fixed points of nonlinear mappings in Hilbert spaces
    • F.E. Browder and W.V. Petryshyn (1967). Construction of fixed points of nonlinear mappings in Hilbert spaces. 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
  • 2
    • 0035351666 scopus 로고    scopus 로고
    • A weak-to-strong convergence principle for Fejér monotone methods in Hilbert space
    • H.H. Bauschke and P.L. Combettes (2001). A weak-to-strong convergence principle for Fejér monotone methods in Hilbert space. Math. Oper. Res. 26:248-264.
    • (2001) Math. Oper. Res , vol.26 , pp. 248-264
    • Bauschke, H.H.1    Combettes, P.L.2
  • 3
    • 0031118954 scopus 로고    scopus 로고
    • Convex set theoretic image recovery by extrapolated iterations of paralell subgradients projections
    • P.L. Combettes (1997). Convex set theoretic image recovery by extrapolated iterations of paralell subgradients projections. IEEE Trans. on Image Processing 6:493-506.
    • (1997) IEEE Trans. on Image Processing , vol.6 , pp. 493-506
    • Combettes, P.L.1
  • 4
    • 4344685262 scopus 로고    scopus 로고
    • Image restoration subject to a. total variation constraint
    • P.L. Combettes and J.C Pesquet (2004). Image restoration subject to a. total variation constraint. IEEE Trans. on Image Processing 13:1213-1222.
    • (2004) IEEE Trans. on Image Processing , vol.13 , pp. 1213-1222
    • Combettes, P.L.1    Pesquet, J.C.2
  • 5
    • 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. 19:33-55.
    • (1998) Numer. Funct. Anal. Optim , vol.19 , pp. 33-55
    • Deutsch, F.1    Yamada, I.2
  • 6
    • 0002125350 scopus 로고    scopus 로고
    • Convex Analysis and Variational Problems
    • SIAM, Philadelphia
    • I. Ekeland and R. Themam (1999). Convex Analysis and Variational Problems. Classic in Applied Mathematics. Vol. 28. SIAM, Philadelphia.
    • (1999) Classic in Applied Mathematics , vol.28
    • Ekeland, I.1    Themam, R.2
  • 7
    • 0003263852 scopus 로고
    • Topics in Metric Fixed Point Theory
    • Cambridge University Press, Cambridge
    • K. Goebel and W.A. Kirk (1990). Topics in Metric Fixed Point Theory. Cambridge Studies in Advanced Mathematics. Vol. 28. Cambridge University Press, Cambridge.
    • (1990) Cambridge Studies in Advanced Mathematics , vol.28
    • Goebel, K.1    Kirk, W.A.2
  • 8
    • 0000595549 scopus 로고
    • On the Mann iteration process in Hilbert spaces
    • T.L. Hicks and J.D. Kubicek (1977). On the Mann iteration process in Hilbert spaces. J. Math. Anal. Appl. 59:498-504.
    • (1977) J. Math. Anal. Appl , vol.59 , pp. 498-504
    • Hicks, T.L.1    Kubicek, J.D.2
  • 9
    • 7544220240 scopus 로고    scopus 로고
    • Strong convergence theorems for nonexpansive nonself-mappings and inverse strongly monotone mappings
    • H. Iiduka and W. Takahashi (2004). Strong convergence theorems for nonexpansive nonself-mappings and inverse strongly monotone mappings. J. Convex Analysis 11:69-79.
    • (2004) J. Convex Analysis , vol.11 , pp. 69-79
    • Iiduka, H.1    Takahashi, W.2
  • 10
    • 84890364931 scopus 로고
    • The common fixed point theory of singlevalued mappings and multivalued mappings
    • S. Itoh and W. Takahashi (1978). The common fixed point theory of singlevalued mappings and multivalued mappings. Pacific J. Math. 79:493-508.
    • (1978) Pacific J. Math , vol.79 , pp. 493-508
    • Itoh, S.1    Takahashi, W.2
  • 11
    • 43149107198 scopus 로고    scopus 로고
    • Convex minimization over the fixed points set of demicontractive mappings
    • P.E. Maingé (2008). Convex minimization over the fixed points set of demicontractive mappings. Positivity 12:269-280.
    • (2008) Positivity , vol.12 , pp. 269-280
    • Maingé, P.E.1
  • 12
    • 52149115452 scopus 로고    scopus 로고
    • P.E. Maingé and A. Moudafi (2007). Strong convergence of an iterative method for hierarchical fixed-point problems. Pacific J. Optimization 3:529-538.
    • P.E. Maingé and A. Moudafi (2007). Strong convergence of an iterative method for hierarchical fixed-point problems. Pacific J. Optimization 3:529-538.
  • 13
    • 33644654188 scopus 로고    scopus 로고
    • A general iterative method for nonexpansive mappings in Hilbert spaces
    • G. Marino and H.K. Xu (2006). A general iterative method for nonexpansive mappings in Hilbert spaces. J. Math. Anal. Appl. 318:43-52.
    • (2006) J. Math. Anal. Appl , vol.318 , pp. 43-52
    • Marino, G.1    Xu, H.K.2
  • 14
    • 33846303213 scopus 로고    scopus 로고
    • Weak and strong convergence theorems for strict pseudocontractions
    • G. Marino and H.K. Xu (2007). Weak and strong convergence theorems for strict pseudocontractions. J. Math. Anal. Appl. 329:336-346.
    • (2007) J. Math. Anal. Appl , vol.329 , pp. 336-346
    • Marino, G.1    Xu, H.K.2
  • 15
    • 84966244659 scopus 로고    scopus 로고
    • The solution by iteration of nonlinear equations in Hilbert spaces
    • S. Maruster (1997). The solution by iteration of nonlinear equations in Hilbert spaces. Proc. Amer. Math. Soc. 63:69-73.
    • (1997) Proc. Amer. Math. Soc , vol.63 , pp. 69-73
    • Maruster, S.1
  • 16
    • 52149098242 scopus 로고    scopus 로고
    • Iterative aproximation of fixed points of demicontractive maps. The Abdus Salam. Intern. Centre for Theoretical Physics, Trieste, November
    • C. Moore (1998). Iterative aproximation of fixed points of demicontractive maps. The Abdus Salam. Intern. Centre for Theoretical Physics, Trieste, Italy, Scientific Report, IC/98/214, November.
    • (1998) Italy, Scientific Report, IC/98/214
    • Moore, C.1
  • 17
    • 0037930573 scopus 로고    scopus 로고
    • Non-strictly convex minimization over the bounded fixed point set of nonexpansive mappings
    • N. Ogura and I. Yamada (2003). Non-strictly convex minimization over the bounded fixed point set of nonexpansive mappings. Numer. Funct. Anal. Optim. 24:129-135.
    • (2003) Numer. Funct. Anal. Optim , vol.24 , pp. 129-135
    • Ogura, N.1    Yamada, I.2
  • 19
    • 77956693893 scopus 로고    scopus 로고
    • The hybrid steepest descent method for the variational inequality over the intersection of fixed point sets of nonexpansive mappings
    • D. Butnariu, Y. Censor, and S. Reich, eds, Elsevier, Amsterdam, pp
    • I. Yamada (2001). The hybrid steepest descent method for the variational inequality over the intersection of fixed point sets of nonexpansive mappings. In: Inherently Parallel Algorithm for Feasibility and Optimization and Their Applications. (D. Butnariu, Y. Censor, and S. Reich, eds.) Elsevier, Amsterdam, pp. 473-504.
    • (2001) Inherently Parallel Algorithm for Feasibility and Optimization and Their Applications , pp. 473-504
    • Yamada, I.1
  • 20
    • 11144241645 scopus 로고    scopus 로고
    • Hybrid steepest descent method for the variational inequality problem over the fixed point set of certain quasi-nonexpansive mappings
    • I. Yamada and N. Ogura (2004). Hybrid steepest descent method for the variational inequality problem over the fixed point set of certain quasi-nonexpansive mappings. Numer. Funct. Anal. Optim. 25:619-655.
    • (2004) Numer. Funct. Anal. Optim , vol.25 , pp. 619-655
    • Yamada, I.1    Ogura, N.2
  • 21
    • 0012580117 scopus 로고    scopus 로고
    • A numerically robust hybrid steepest descent method for the convexly constrained generalized inverse problems
    • Inverse Problems, Image Analysis and Medical Imaging, Z. Nashed and O. Scherzer, eds
    • I. Yamada, N. Ogura, and N. Shirakawa (2002). A numerically robust hybrid steepest descent method for the convexly constrained generalized inverse problems. In: Inverse Problems, Image Analysis and Medical Imaging. (Z. Nashed and O. Scherzer, eds.) Contemporary Mathematics. Vol. 313. pp. 269-305.
    • (2002) Contemporary Mathematics , vol.313 , pp. 269-305
    • Yamada, I.1    Ogura, N.2    Shirakawa, N.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.