Error Bound Estimation For The Generalized Variational Inequalities And Complementarity Problem Over A Polyhedron Cone

The thesis mainly considers the error bound for the generalized linear complementarity problem, the generalized nonlinear complementarity problem, and the generalized variational inequalities problem over a polyhedral cone, respectively. It comprises the following three chapters.Chapter 1 gives an introduction of the thesis, which mainly discusses the current development on error bound for linear complementarity problem, nonlinear complementarity problem and variational inequalities problem, respectively, and furthermore, the main contribution of this paper is also listed.in this chapter.In Chapter 2, we consider the error bound and the auxiliary problem algorithm for the generalized linear complementarity problem over a polyhedral cone(GLCP): First, we give an absolute and a relative global error bound for GLCP and nondegenerate GLCP, respectively, and then we explore the properties of the solution set of the problem, based on which we establish another absolute and relative error bound for GLCP which is much exacter compared with the result above. Finally, we develop the auxiliary method for solving the GLCP which converges globally under the suitable conditions.In chapter 3, we consider the error bound for generalized variational inequalities (GVIP) and generalized nonlinear complementarity problem (GNCP) over a closed convex polyhedral cone. Based on the natural residue, we establish a global absolute error bound and a global relative error bound for GVIP with γ-...