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Zbl 1057.49011
Han, Derek; Sun, Wenyu
A new modified Goldstein-Levitin-Polyak projection method for variational inequality problems. (English)
[J] Comput. Math. Appl. 47, No. 12, 1817-1825 (2004). ISSN 0898-1221

Summary: We first show that the adjustment parameter in the step size choice strategy of the modified Goldstein-Levitin-Polyak projection method proposed by He et al. for asymmetric strongly monotone variational inequality problems can be bounded away from zero by a positive constant. Under this observation, we propose a new step size rule which seems to be more practical and robust than the original one. We show that the new modified method is globally convergent under the same conditions and report some computational results to illustrate the method.

MSC 2000:: *49J40 Variational methods including variational inequalities

Keywords: global convergence; variational inequality; strongly monotone mapping; projection methods

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Zentralblatt MATH Berlin [Germany]