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.


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