Iterative methods for solving general quasi-variational inequalities

作者：Noor Muhammad Aslam^*; Noor Khalida Inayat; Al Said Eisa

来源：Optimization Letters, 2010, 4(4): 513-530.

DOI：10.1007/s11590-010-0180-3

• Variational inequalities
• Nonconvex functions
• Fixed-point problem
• Wiener-Hopf equations
• Projection operator
• Convergence

In this paper, we introduce a new class of variational inequalities, which is called the general quasi-variational inequality. We establish the equivalence among the general quasi variational inequality and implicit fixed point problems and the Wiener-Hopf equations. We use this equivalent formulation to discuss the existence of a solution of the general quasi-variational inequality. This equivalent formulation is used to suggest and analyze some iterative algorithms for solving the general quasi-variational inequality. We also discuss the convergence analysis of these iterative methods. Several special cases are also discussed.