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Application of penalty methods to non-stationary variational inequalities |
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| Institution: | 1. Toulouse School of Economics and CEPR, France;2. Catholic University of Milan, Italy;1. Electrochemical Energy Storage and Conversion Laboratory, Department of Mechanical, Aerospace, and Biomedical Engineering, The University of Tennessee, Knoxville, TN 37996, USA;2. School of Mechanical Engineering, Hanyang University, Seoul 133-791, South Korea;3. Energy and Transportation Science Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA;1. The Key Laboratory of Advanced Manufacturing Technology, Beijing University of Technology, Beijing, China;2. Beijing Engineering Research Center of Precision Measurement Technology and Instruments, Beijing University of Technology, Beijing, China |
| Abstract: | We solve a general 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 utilize a sequence of solutions of auxiliary problems based on a penalty method. Its convergence is attained without concordance of penalty and approximation parameters under mild coercivity type conditions. We also show that the regularized version of the penalty method enables us to further weaken the coercivity condition. |
| Keywords: | Variational inequality Non-stationarity Non-monotone mappings Approximation sequence Penalty method Regularization Coercivity conditions |
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