Some iterative algorithms for solving mixed variational inequalities. (English) Zbl 1269.49005

Bnouhachem, Abdellah; Noor, M. Aslam; Massaq, Abdellah; Zhaohan, Sheng

J. Adv. Math. Stud. 5, No. 2, 1-12 (2012).

Summary: In this paper, we propose two new methods for solving mixed quasi-variational inequalities using the resolvent operator technique. Under certain conditions, the global convergence of both methods is proved. The skew-symmetry of the nonlinear bifunction plays a crucial part in the convergence analysis of these new iterative methods. The comparison of these methods with other methods for solving mixed quasi-variational inequalities is an interesting open problem.

MSC:

49J40	Variational inequalities
49M25	Discrete approximations in optimal control
47J25	Iterative procedures involving nonlinear operators
47H05	Monotone operators and generalizations
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Keywords:

mixed quasi-variational inequalities; self-adaptive rules; pseudomonotone operators; resolvent operator