Abstract
In a Hilbert space, we study the convergence of the subgradient method to a common solution of a finite family of variational inequalities and of a finite family of fixed point problems under the presence of computational errors. The convergence of the subgradient method is established for nonsummable computational errors. We show that the subgradient method generates a good approximate solution, if the sequence of computational errors is bounded from above by a constant.
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References
Zaslavski AJ (2013) The extragradient method for finding a common solution of a finite family of variational inequalities and a finite family of fixed point problems in the presence of computational errors. J Math Anal Appl 400:651–663
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© 2016 Springer International Publishing Switzerland
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Zaslavski, A.J. (2016). A Common Solution of a Family of Variational Inequalities. In: Numerical Optimization with Computational Errors. Springer Optimization and Its Applications, vol 108. Springer, Cham. https://doi.org/10.1007/978-3-319-30921-7_13
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DOI: https://doi.org/10.1007/978-3-319-30921-7_13
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-30920-0
Online ISBN: 978-3-319-30921-7
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