The Extragradient Method for Solving Variational Inequalities in the Presence of Computational Errors

A. J. Zaslavski ()
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A. J. Zaslavski: Technion

Journal of Optimization Theory and Applications, 2012, vol. 153, issue 3, No 4, 602-618

Abstract: Abstract In a Hilbert space, we study the convergence of the subgradient method to a solution of a variational inequality, under the presence of computational errors. Most results known in the literature establish convergence of optimization algorithms, when computational errors are summable. In the present paper, the convergence of the subgradient method for solving variational inequalities 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.

Keywords: Computational error; Hilbert space; Subgradient method; Variational inequality (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10957-011-9975-3

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