Geodesic
Viscosity approximation method for a variational problem
May, R.1
1 Mathematics Department, College of Science, King Faisal University, P.O. 380, Ahsaa 31982, Kingdom of Saudi Arabia
Journal of nonlinear sciences and its applications, Tome 16 (2023) no. 4, p. 208-221.

Voir la notice de l'article provenant de la source International Scientific Research Publications

By combining the works of Moudafi [A. Moudafi, J. Math. Anal. Appl., $\textbf{241}$ (2000), 46--55] and Iiduka and Takahashi [H. Iiduka, W. Takahashi, Nonlinear Anal., $\textbf{61}$ (2005), 341--350], we introduce an iterative process that converges strongly to a particular solution of a variational inequality problem. We also study the stability of the algorithm under relatively small perturbation and we apply the obtained results to the study of a constrained optimization problem and a problem of common fixed points of two nonexpansive mappings. Some numerical experiments are provided to study the affect of some parameters on the speed of the convergence of the considered algorithm.
DOI : 10.22436/jnsa.016.04.02
Classification : 47H09, 47H05, 47H10, 47J20
Keywords: Hilbert spaces, variational inequality problem, nonexpansive mapping, inverse strongly monotone mappings

May, R. 1

1 Mathematics Department, College of Science, King Faisal University, P.O. 380, Ahsaa 31982, Kingdom of Saudi Arabia 
@article{JNSA_2023_16_4_a1,
     author = {May, R.},
     title = {Viscosity approximation method for a variational problem},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {208-221},
     publisher = {mathdoc},
     volume = {16},
     number = {4},
     year = {2023},
     doi = {10.22436/jnsa.016.04.02},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.016.04.02/}
}
TY  - JOUR
AU  - May, R.
TI  - Viscosity approximation method for a variational problem
JO  - Journal of nonlinear sciences and its applications
PY  - 2023
SP  - 208
EP  - 221
VL  - 16
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.016.04.02/
DO  - 10.22436/jnsa.016.04.02
LA  - en
ID  - JNSA_2023_16_4_a1
ER  - 
%0 Journal Article
%A May, R.
%T Viscosity approximation method for a variational problem
%J Journal of nonlinear sciences and its applications
%D 2023
%P 208-221
%V 16
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.016.04.02/
%R 10.22436/jnsa.016.04.02
%G en
%F JNSA_2023_16_4_a1
May, R. Viscosity approximation method for a variational problem. Journal of nonlinear sciences and its applications, Tome 16 (2023) no. 4, p. 208-221. doi : 10.22436/jnsa.016.04.02. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.016.04.02/

[1] Bauschke, H. H.; Combettes, P. L. Convex analysis and monotone operator theory in Hilbert spaces, In: CMS Books in Mathematics/Ouvrages de Math´ematiques de la SMC, Springer, New York, 2011 | DOI | Zbl

[2] Bertsekas, D. P. Nonlinear programming, J. Oper. Res. Soc., Volume 48 (1997), p. 334-334

[3] Cholamjiak, P.; Kesornprom, S.; Pholasa, N. Weak and strong convergence theorems for the inclusion problem and the fixed-point problem of nonexpansive mapping, Mathematics, Volume 7 (2019), pp. 1-19 | DOI

[4] uler, O. G¨ Foundations of optimization, Springer, New York, 2010 | DOI

[5] Iiduka, H.; Takahashi, W. Strong convergence theorems for nonexpansive mapping and inverse-strongly monotone mappings, Nonlinear Anal., Volume 61 (2005), pp. 341-350 | DOI | Zbl

[6] Moudafi, A. Viscosity approximation methods for fixed-points problems, J. Math. Anal. Appl., Volume 241 (2000), pp. 46-55 | Zbl | DOI

[7] Peypoquet, J. Convex optimization in normed spaces: theory, methods and examples, Springer Briefs Optim., Springer, Cham, 2015 | Zbl

[8] Plubteing, S.; Kumam, P. Weak convergence theorem for monotone mappings and a countable family of nonexpansive mappings, J. Comput. Appl. Math., Volume 224 (2009), pp. 614-621 | Zbl | DOI

[9] Takahashi, W.; Toyoda, M. Weak convergence theorems for nonexpansive mappings and monotone mappings, J. Optim. Theory Appl., Volume 118 (2003), pp. 417-428 | DOI

[10] Ugwunnadi, G. C. Viscosity approximation method for solving variational inequality problem in real Banach spaces, Armen. J. Math., Volume 13 (2021), pp. 1-20 | DOI

[11] Wang, Y.; Pan, C. Viscosity approximation methods for a general variational inequality system and fixed point problems in Banach spaces, Symmetry, Volume 12 (2020), pp. 1-15 | DOI

[12] Xu, H.-K. Iterative algorithms for nonlinear operators, J. London Math. Soc. (2), Volume 66 (2002), pp. 240-256 | DOI

[13] Xu, H.-K. Averaged mapping and the gradient-projection algorithm, J. Optim. Theory Appl., Volume 150 (2011), pp. 360-378 | Zbl | DOI

[14] Yao, Y.; Liou, Y.-C.; Chen, C.-P. Algorithms construction for nonexpansive mappings and inverse-strongly monotone mappings, Taiwanese J. Math., Volume 15 (2011), pp. 1979-1998 | DOI | Zbl

[15] Yazdi, M.; Sababe, S. H. A viscosity approximation methods for solving general system of variational inequalities, generalized mixed equilibrium problems and fixed point problems, Symmetry, Volume 14 (2022), pp. 1-23 | DOI

Cité par Sources :