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Resolvent dynamical systems and mixed variational inequalities. (English) Zbl 1415.49005

Summary: In this paper, we use the dynamical systems technique to suggest and investigate some inertial proximal methods for solving mixed variational inequalities and related optimization problems. It is proved that the convergence analysis of the proposed methods requires only the monotonicity. Some special cases are also considered. Our method of proof is very simple as compared with other techniques. Ideas and techniques of this paper may be extended for other classes of variational inequalities and equilibrium problems.

MSC:

49J40 Variational inequalities
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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