Iterative algorithms with the regularization for the constrained convex minimization problem and maximal monotone operators

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.

Keywords:

• Constrained convex minimization
• resolvent operator
• maximal monotone operators

Acknowledgements

The authors appreciated the referees for providing valuable comments improving the content of this research paper. The second author would like to thank the Research and Innovation Services of King Mongkut’s Institute of Technology Ladkrabang.

Notes

No potential conflict of interest was reported by the authors.