Algorithms For General Set-valued Quasi-variational Inequalities And Quasi-complementarity Problems

In this thesis we are concerned about algorithms for general set-valued quasi-variational inequalities and quasi-complementarity problems. We note that one of the most important and difficult problems in variational inequality theory is to develop an efficient and implementable iterative algorithm for solving various classes of variational inequalities and variational inclusions. A topic of my thesis is to consider the new algorithms and improvement of algorithms for general set-valued quasi-variational inequalities and quasi-complementarity problems. In addition, we prove the existence of solutions for the class of general set-valued quasi-variational inequalities and quasi-complementarity problems and discuss the convergence of iterative sequences generated by iterative algorithms.In detail, we prepare five chapters for our topics in this thesis. The first chapter serves as an introduction to this thesis which involves the summary of my work. The second chapter mainly concerns about Siddiqi-Ansari theorem and algorithms for general generalized nonlinear set-valued mixed quasi-variational inequalities, Nadler Lemma and algorithms for general generalized nonlinear set-valued mixed quasi-variational inequalities is presented in the next chapter. In chapter four, we discuss a class of multi-valued quasi-complementarity problems. Finally, we present the review and outlook of my work.