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New inexact implicit method for general mixed quasi variational inequalities

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Abstract

In this paper, we suggest and analyze a new self-adaptive inexact implicit method with a variable parameter for general mixed quasi variational inequalities, where the skew-symmetry of the nonlinear bifunction plays a crucial part in the convergence analysis of this method. We use a self-adaptive technique to adjust parameter ρ at each iteration. The global convergence of the proposed method is proved under some mild conditions. Preliminary numerical results indicate that the self-adaptive adjustment rule is necessary in practice.

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Correspondence to Muhammad Aslam Noor.

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Muhammad Aslam Noor is supported by the Higher Education Commission, Pakistan, through research grant No: 1-28/HEC/HRD/2005/90.

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Bnouhachem, A., Noor, M.A. New inexact implicit method for general mixed quasi variational inequalities. J Glob Optim 44, 409–421 (2009). https://doi.org/10.1007/s10898-008-9339-1

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  • DOI: https://doi.org/10.1007/s10898-008-9339-1

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