Several Methods For General Variational Inequalities

General variational inequality was introduced and studied by Noor in 1988. Many problems in pure and applied sciences, such as equilibrium problems, nonlinear nonconvex programing, quasi-variational inequality problems and engineering sciences et.al., can be studied in the framework of general variational inequalities. Two forms of general variational inequality problems are studied in this thesis and new methods proposed, respectivly.Four chapters are included in this dissertation.Chapter 1 is the introduction, which mainly contains the definition of general variational inequalities, research valuations and research situations. In this chapter, we also discuss the projection-type methodsthe and the splitting methods (implicit methods) for general variational inequality problems. Furthermore, the main task and related indispensable knowledge are also presented in brief.In Chapter 2, a new projection-type method for general variational inequalities is proposed. On the basis of a new search direction d_k in which d_k = —{T(u~k)+ρT{ω~k)}, a new method for general variational inequalities is presented. Under the mild conditions that T is pseudo-monotone and g is nonsingular, we prove the global convergence of the new method. In the end, we notice that if ρ is relaxed to ρk, the convergence of the new method can also be proved.In chapter 3, we study the self-adaptive operator splitting methods for general monotone variational inequalities and present a new method for general vari-...