Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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A VISCOSITY TYPE PROJECTION METHOD FOR SOLVING PSEUDOMONOTONE VARIATIONAL INEQUALITIES

  • Muangchoo, Kanikar (Department of Mathematics and Statistics, Faculty of Science and Technology Rajamangala University of Technology Phra Nakhon (RMUTP))
  • Received : 2020.09.28
  • Accepted : 2021.03.31
  • Published : 2021.06.15
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Abstract

A plethora of applications from mathematical programmings, such as minimax, mathematical programming, penalization and fixed point problems can be framed as variational inequality problems. Most of the methods that used to solve such problems involve iterative methods, that is why, in this paper, we introduce a new extragradient-like method to solve pseudomonotone variational inequalities in a real Hilbert space. The proposed method has the advantage of a variable step size rule that is updated for each iteration based on previous iterations. The main advantage of this method is that it operates without the previous knowledge of the Lipschitz constants of an operator. A strong convergence theorem for the proposed method is proved by letting the mild conditions on an operator 𝒢. Numerical experiments have been studied in order to validate the numerical performance of the proposed method and to compare it with existing methods.

Keywords

Acknowledgement

This project was supported by Rajamangala University of Technology Phra Nakhon (RMUTP).

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