## Numerical method for general mixed quasi-variational inequalities.(English)Zbl 1157.65037

Summary: We use the resolvent operator to suggest and analyze a new numerical method for solving general mixed quasi-variational inequalities coupled with a new direction and a new step size $$\alpha _k$$. Under certain conditions, the global convergence of the proposed method is proved. Some preliminary computational results are given to illustrate the efficiency of the proposed method. Since the general mixed quasi-variational inequalities include general variational inequalities, quasi-variational inequalities and nonlinear (implicit) complementarity problems as special cases, results proved in this paper continue to hold for these problems. Results proved in this paper may be viewed as a refinement of the previous known results.

### MSC:

 65K10 Numerical optimization and variational techniques 49J40 Variational inequalities 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) 49M30 Other numerical methods in calculus of variations (MSC2010)
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