Iterative algorithms with regularization for hierarchical variational inequality problems and convex minimization problems

Lu Chuan Ceng; Suliman Al-Homidan; Qamrul Hasan Ansari

doi:10.1186/1687-1812-2013-284

Iterative algorithms with regularization for hierarchical variational inequality problems and convex minimization problems

Lu Chuan Ceng
, Suliman Al-Homidan^*
, Qamrul Hasan Ansari

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this paper, we consider a variational inequality problem which is defined over the set of intersections of the set of fixed points of a ζ-strictly pseudocontractive mapping, the set of fixed points of a nonexpansive mapping and the set of solutions of a minimization problem. We propose an iterative algorithm with regularization to solve such a variational inequality problem and study the strong convergence of the sequence generated by the proposed algorithm. The results of this paper improve and extend several known results in the literature.

Original language	English
Article number	284
Journal	Fixed Point Theory and Algorithms for Sciences and Engineering
Volume	2013
DOIs	https://doi.org/10.1186/1687-1812-2013-284
State	Published - Nov 2013

Bibliographical note

Funding Information:
In this research, second and third author were supported by King Fahd University of Petroleum & Minerals project number IN101009. The first author was partially supported by the National Science Foundation of China (11071169), Innovation Program of Shanghai Municipal Education Commission (09ZZ133) and Leading Academic Discipline Project of Shanghai Normal University (DZL707). The research part of third author was done during his visit to King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia.

ASJC Scopus subject areas

Geometry and Topology
Applied Mathematics

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title = "Iterative algorithms with regularization for hierarchical variational inequality problems and convex minimization problems",

abstract = "In this paper, we consider a variational inequality problem which is defined over the set of intersections of the set of fixed points of a ζ-strictly pseudocontractive mapping, the set of fixed points of a nonexpansive mapping and the set of solutions of a minimization problem. We propose an iterative algorithm with regularization to solve such a variational inequality problem and study the strong convergence of the sequence generated by the proposed algorithm. The results of this paper improve and extend several known results in the literature.",

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note = "Funding Information: In this research, second and third author were supported by King Fahd University of Petroleum \& Minerals project number IN101009. The first author was partially supported by the National Science Foundation of China (11071169), Innovation Program of Shanghai Municipal Education Commission (09ZZ133) and Leading Academic Discipline Project of Shanghai Normal University (DZL707). The research part of third author was done during his visit to King Fahd University of Petroleum \& Minerals, Dhahran, Saudi Arabia. ",

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AU - Al-Homidan, Suliman

AU - Ansari, Qamrul Hasan

N1 - Funding Information: In this research, second and third author were supported by King Fahd University of Petroleum & Minerals project number IN101009. The first author was partially supported by the National Science Foundation of China (11071169), Innovation Program of Shanghai Municipal Education Commission (09ZZ133) and Leading Academic Discipline Project of Shanghai Normal University (DZL707). The research part of third author was done during his visit to King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia.

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N2 - In this paper, we consider a variational inequality problem which is defined over the set of intersections of the set of fixed points of a ζ-strictly pseudocontractive mapping, the set of fixed points of a nonexpansive mapping and the set of solutions of a minimization problem. We propose an iterative algorithm with regularization to solve such a variational inequality problem and study the strong convergence of the sequence generated by the proposed algorithm. The results of this paper improve and extend several known results in the literature.

AB - In this paper, we consider a variational inequality problem which is defined over the set of intersections of the set of fixed points of a ζ-strictly pseudocontractive mapping, the set of fixed points of a nonexpansive mapping and the set of solutions of a minimization problem. We propose an iterative algorithm with regularization to solve such a variational inequality problem and study the strong convergence of the sequence generated by the proposed algorithm. The results of this paper improve and extend several known results in the literature.

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JO - Fixed Point Theory and Algorithms for Sciences and Engineering

JF - Fixed Point Theory and Algorithms for Sciences and Engineering

M1 - 284

ER -

Iterative algorithms with regularization for hierarchical variational inequality problems and convex minimization problems

Abstract

Bibliographical note

ASJC Scopus subject areas

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