Some Results on Strongly Pseudomonotone Quasi-Variational Inequalities

  • Luong V. Nguyen
  • Xiaolong QinEmail author


In this paper, strongly pseudomonotone quasi-variational inequalities are investigated. We provide sufficient conditions for existence and uniqueness of solutions of strongly pseudomonotone quasi-variational inequalities. We present some error bounds in terms of residual and regularized gap functions. The global exponential stability of equilibrium solutions of a projected dynamical system for strongly pseudomonotone quasi-variational inequalities is investigated. Strong convergence and error estimates for sequence generated by the (modified) gradient projection method with suitable choices of stepsizes are also studied. Some examples and numerical experiments are provided to support our main results.


Quasi-variational inequalities Strong pseudomonotonicity Projection method Error bounds Dynamical systems 

Mathematics Subject Classification (2010)

49J40 47J20 49M30 


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This article was supported by the National Natural Science Foundation of China under Grant No.11401152. The first author was also supported by the Research Fund for International Young Scientists under Grant No. 1181101157 and the China Postdoctoral Science Foundation under Grant No. 2017M6200421.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Institute of Fundamental and Frontier SciencesUniversity of Electronic Science and Technology of ChinaChengduChina
  2. 2.Department of Natural SciencesHong Duc UniversityThanh HoaVietnam

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