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Comparison of two kinds of prediction-correction methods for monotone variational inequalities. (English) Zbl 1061.90111
Summary: We study the relationship between the forward-backward splitting method and the extra-gradient method for monotone variational inequalities. Both of the methods can be viewed as prediction-correction methods. The only difference is that they use different search directions in the correction-step. Our analysis explains theoretically why the extra-gradient methods usually outperform the forward-backward splitting methods. We suggest some modifications for the two methods and numerical results are given to verify the superiority of the modified methods.

MSC:
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
49J40Variational methods including variational inequalities
90C52Methods of reduced gradient type