On the Weak Convergence of the Extragradient Method for Solving Pseudo-Monotone Variational Inequalities

Phan Tu Vuong ()
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Phan Tu Vuong: Vienna University of Technology

Journal of Optimization Theory and Applications, 2018, vol. 176, issue 2, No 7, 399-409

Abstract: Abstract In infinite-dimensional Hilbert spaces, we prove that the iterative sequence generated by the extragradient method for solving pseudo-monotone variational inequalities converges weakly to a solution. A class of pseudo-monotone variational inequalities is considered to illustrate the convergent behavior. The result obtained in this note extends some recent results in the literature; especially, it gives a positive answer to a question raised in Khanh (Acta Math Vietnam 41:251–263, 2016).

Keywords: Variational inequality; Extragradient method; Pseudo-monotonicity; Weak convergence; 47J20; 49J40; 49M30 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10957-017-1214-0

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