Resolvent dynamical systems and mixed variational inequalities

Volume 10, Issue 6, pp 2925--2933 http://dx.doi.org/10.22436/jnsa.010.06.07

Publication Date: June 25, 2017 Submission Date: February 13, 2017

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Authors

Bandar Bin-Mohsin - Department of Mathematics, King Saud University, Riyadh, Saudi Arabia. Muhammad Aslam Noor - Department of Mathematics, King Saud University, Riyadh, Saudi Arabia. - Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan. Khalida Inayat Noor - Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan. Rafia Latif - Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan.

Abstract

In this paper, we use the dynamical systems technique to suggest and investigate some inertial proximal methods for solving mixed variational inequalities and related optimization problems. It is proved that the convergence analysis of the proposed methods requires only the monotonicity. Some special cases are also considered. Our method of proof is very simple as compared with other techniques. Ideas and techniques of this paper may be extended for other classes of variational inequalities and equilibrium problems.

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Keywords

• Variational inequalities
• dynamical systems
• inertial proximal methods
• convergence.

MSC

•  26D15
•  26D10
•  90C23
•  49J40

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