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Inertial proximal method for mixed quasi variational inequalities. (English) Zbl 1045.49012

Summary: In this paper, we use the auxiliary principle technique to suggest and analyze an inertial proximal method for a class of mixed quasivariational inequalities. We have shown that the convergence of the proposed method requires only pseudomonotonicity, which is a weaker condition than monotonicity. The proposed method includes the classical proximal method as a special case. Since the mixed quasivariational inequalities include variational and complementarity problems as special cases, the result proved in this paper continue to hold for these problems.

MSC:

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