Iterative algorithms for a new class of extended general nonconvex set-valued variational inequalities

作者：Alimohammady M; Balooee J; Cho Y J^*; Roohi M

来源：Nonlinear Analysis-Theory Methods & Applications, 2010, 73(12): 3907-3923.

DOI：10.1016/j.na.2010.08.022

• Variational inequalities
• Wiener-Hopf inclusions
• Iterative algorithm
• Monotone operators
• Prox-regularity
• Convergence analysis

Some new classes of extended general nonconvex set-valued variational inequalities and the extended general Wiener-Hopf inclusions are introduced. By the projection technique, equivalence between the extended general nonconvex set-valued variational inequalities and the fixed point problems as well as the extended general nonconvex Wiener-Hopf inclusions is proved. Then by using this equivalent formulation, we discuss the existence of solutions of the extended general nonconvex set-valued variational inequalities and construct some new perturbed finite step projection iterative algorithms with mixed errors for approximating the solutions of the extended general nonconvex set-valued variational inequalities. We also verify that the approximate solutions obtained by our algorithms converge to the solutions of the extended general nonconvex set-valued variational inequalities. The results presented in this paper extend and improve some known results from the literature.

• 出版日期2010-12-15