Abstract
We consider a set-valued (generalized) variational inequality problem in a finite-dimensional setting, where only approximation sequences are known instead of exact values of the cost mapping and feasible set. We suggest to apply a sequence of inexact solutions of auxiliary problems involving general penalty functions. Its convergence is attained without concordance of penalty, accuracy, and approximation parameters under certain coercivity type conditions.
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Konnov, I.V. An Inexact Penalty Method for Non Stationary Generalized Variational Inequalities. Set-Valued Var. Anal 23, 239–248 (2015). https://doi.org/10.1007/s11228-014-0293-4
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DOI: https://doi.org/10.1007/s11228-014-0293-4
Keywords
- Variational inequality
- Non-stationarity
- Non-monotone mappings
- Set-valued mappings
- Approximate solutions
- Penalty method
- Coercivity conditions