Iterative algorithms with the regularization for the constrained convex minimization problem and maximal monotone operators. (3rd October 2017)

• Record Type: Journal Article
• Authors: Khuangsatung, Wongvisarut; Kangtunyakarn, Atid
• Is Part Of: Optimization. Volume 66:Number 10(2017)
• Page Start: 1623
• Page End: 1646
• Publication Date: 2017-10-03
• Subjects: Constrained convex minimization -- resolvent operator -- maximal monotone operators; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1343330
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: In this paper, we prove a strong convergence theorem for finding a common element of the solution set of a constrained convex minimization problem and the set of solutions of a finite family of variational inclusion problems in Hilbert space. A strong convergence theorem for finding a common element of the solution set of a constrained convex minimization problem and the solution sets of a finite family of zero points of the maximal monotone operator problem in Hilbert space is also obtained. Using our main result, we have some additional results for various types of non-linear problems in Hilbert space.