Yıl 2020,
Cilt: 3 Sayı: 1, 1 - 11, 31.03.2020
Thierno Sow
,
Cheikh Diop
Mouhamadou Moustapha Gueye
Kaynakça
- Alber, Ya., Metric and generalized Projection Operators in Banach space:propertiesand applications in Theory and Applications of Nonlinear Operators of Accretive andMonotone Type,(A. G Kartsatos, Ed.), Marcel Dekker, New York (1996), pp. 15-50.
- Aoyama, K., Iiduka, H., Takahashi, W., Weak convergence of an iterative sequencefor accretive operators in Banach spaces, Fixed Point Theory Appl. 2006 (2006)doi:10.1155/FPTA/2006/35390. Article ID 35390, 13 pages. Noor, M.A., Some development in general variational inequalities, Appl. Math. Com-put. 152 (2004) 199-277.
- Browder, F. E., Convergenge theorem for sequence of nonlinear operator in Banachspaces, Z., 100 (1967) 201-225.
- Ceng, L. C., Yao, J. C., An extragradient-like approximation method for variationalinequality problems and fixed point problems, Appl. Math. Comput., 190 (2007),205-215.
- Censor, Y., Iusem, A.N., Zenios, S.A., An interior point method with Bregman func-tions for the variational inequality problem with paramonotone operators, Math.Program. 81 (1998) 373-400.
- Cioranescu, I., Geometry of Banach space, duality mapping and nonlinear problems,Kluwer, Dordrecht, (1990).
- Chang, S., Kim, J. K., Wang, X. R., Modified block iterative algorithm for solvingconvex feasibility problems in Banach spaces, Journal of Inequalities and Applications,vol. (2010), Article ID 869684, 14 pages.
- Chidume, C. E., Geometric Properties of Banach spaces and Nonlinear Iterations,Springer Verlag Series: Lecture Notes in Mathematics, Vol. 1965,(2009), ISBN 978-1-84882-189.
- Goebel, K., Kirk, W. A., Topics in metric fixed poit theory, Cambridge Studies, inAdvanced Mathemathics, 28, University Cambridge Press, Cambridge 1990.
- Kotzer, T., Cohen, N., Shamir, J., Images to ration by a novel method of parallelprojection onto constraint sets, Optim. Lett., 20 (1995), 1172-1174.
- Mainge, P. E., Strong convergence of projected subgradient methods for nonsmoothand nonstrictly convex minimization, Set-Valued Analysis, 16, 899-912 (2008).
- Marino, G., Xu, H. K., A general iterative method for nonexpansive mappings inHibert spaces, J. Math. Anal. Appl. 318 (2006), 43-52.
- Moudafi, A., Viscosity approximation methods for fixed-point problems, J. Math.Anal. Appl. 241 (2000), 46-55.
- Opial, Z., Weak convergence of sequence of succecive approximation of nonexpansivemapping, Bull. Am. Math. Soc. 73 (1967), 591 597.
- Qin, X., Kang, S. M., Convergence theorems on an iterative method for variational in-equality problems and fixed point problems, Bull. Malays. Math. Sci. Soc., 33 (2010),155-167.
- Sow, T.M.M., A new general iterative algorithm for solving a variational inequalityproblem with a quasi-nonexpansive mapping in Banach spaces, Communications inOptimization Theory, Vol. 2019 (2019), Article ID 9, pp. 1-12.
- Xu, H.K., Kim, T.H., Convergence of hybrid steepest-descent methods for variationalinequalities, J. Optim. Theory Appl. 119 (2003) 185-201.
- Xu, H.K., An iterative approach to quadratic optimization, J. Optim. Theory Appl.116 (2003) 659-678.
General iterative algorithm for solving system of variational inequality problems in real Banach spaces
Yıl 2020,
Cilt: 3 Sayı: 1, 1 - 11, 31.03.2020
Thierno Sow
,
Cheikh Diop
Mouhamadou Moustapha Gueye
Öz
In this paper, we introduce general approximation method for solving system of variational inequality problems in Banach spaces. The strong convergence of this general iterative method is proved under certain assumptions imposed on the sequence of parameters. Application to quadratic optimization problem is also considered. The results presented in the paper extend and improve some recent results announced in the current literature.
Kaynakça
- Alber, Ya., Metric and generalized Projection Operators in Banach space:propertiesand applications in Theory and Applications of Nonlinear Operators of Accretive andMonotone Type,(A. G Kartsatos, Ed.), Marcel Dekker, New York (1996), pp. 15-50.
- Aoyama, K., Iiduka, H., Takahashi, W., Weak convergence of an iterative sequencefor accretive operators in Banach spaces, Fixed Point Theory Appl. 2006 (2006)doi:10.1155/FPTA/2006/35390. Article ID 35390, 13 pages. Noor, M.A., Some development in general variational inequalities, Appl. Math. Com-put. 152 (2004) 199-277.
- Browder, F. E., Convergenge theorem for sequence of nonlinear operator in Banachspaces, Z., 100 (1967) 201-225.
- Ceng, L. C., Yao, J. C., An extragradient-like approximation method for variationalinequality problems and fixed point problems, Appl. Math. Comput., 190 (2007),205-215.
- Censor, Y., Iusem, A.N., Zenios, S.A., An interior point method with Bregman func-tions for the variational inequality problem with paramonotone operators, Math.Program. 81 (1998) 373-400.
- Cioranescu, I., Geometry of Banach space, duality mapping and nonlinear problems,Kluwer, Dordrecht, (1990).
- Chang, S., Kim, J. K., Wang, X. R., Modified block iterative algorithm for solvingconvex feasibility problems in Banach spaces, Journal of Inequalities and Applications,vol. (2010), Article ID 869684, 14 pages.
- Chidume, C. E., Geometric Properties of Banach spaces and Nonlinear Iterations,Springer Verlag Series: Lecture Notes in Mathematics, Vol. 1965,(2009), ISBN 978-1-84882-189.
- Goebel, K., Kirk, W. A., Topics in metric fixed poit theory, Cambridge Studies, inAdvanced Mathemathics, 28, University Cambridge Press, Cambridge 1990.
- Kotzer, T., Cohen, N., Shamir, J., Images to ration by a novel method of parallelprojection onto constraint sets, Optim. Lett., 20 (1995), 1172-1174.
- Mainge, P. E., Strong convergence of projected subgradient methods for nonsmoothand nonstrictly convex minimization, Set-Valued Analysis, 16, 899-912 (2008).
- Marino, G., Xu, H. K., A general iterative method for nonexpansive mappings inHibert spaces, J. Math. Anal. Appl. 318 (2006), 43-52.
- Moudafi, A., Viscosity approximation methods for fixed-point problems, J. Math.Anal. Appl. 241 (2000), 46-55.
- Opial, Z., Weak convergence of sequence of succecive approximation of nonexpansivemapping, Bull. Am. Math. Soc. 73 (1967), 591 597.
- Qin, X., Kang, S. M., Convergence theorems on an iterative method for variational in-equality problems and fixed point problems, Bull. Malays. Math. Sci. Soc., 33 (2010),155-167.
- Sow, T.M.M., A new general iterative algorithm for solving a variational inequalityproblem with a quasi-nonexpansive mapping in Banach spaces, Communications inOptimization Theory, Vol. 2019 (2019), Article ID 9, pp. 1-12.
- Xu, H.K., Kim, T.H., Convergence of hybrid steepest-descent methods for variationalinequalities, J. Optim. Theory Appl. 119 (2003) 185-201.
- Xu, H.K., An iterative approach to quadratic optimization, J. Optim. Theory Appl.116 (2003) 659-678.