Algorithm And Convergence For A Class Of Generalized The Variational Inequality And Complementarity Problem With Set-valued

In this dissertation, some topics, such as global error bound and a new pro-jection algorithm for variational inequality with multi-valued mapping, global errorbound and Levenberg-Marquart algorithm for generalized nonlinear complementar-ity problem with multi-valued mapping, a non-interior path following algorithm forthe generalized linear complementarity problem over a polyhedral cone, are investi-gated. This dissertation is divided into four chapters.In chapter one, we firstly introduced the research background and researchstatus of variational inequality, then we give some definitions and lemmas for thefollowing analysis.In chapter two, firstly, we establish a global error bound estimation for varia-tional inequality with set-valued mapping, to this end, we propose a new projectionalgorithm for variational inequality with set-valued mapping, and the iteration se-quence generated by the algorithm is proven to converge to a solution.In chapter three, we establish a global error bound estimation for general-ized nonlinear complementarity problem with set-valued mapping, according to theFischer function, we obtain another form error bound for generalized nonlinear com-plementarity problem with set-valued mapping, and based on this error bound, aLevenberg-Marquart algorithm is employed for obtaining its solution, and we showthat our algorithm is convergent locally without non-degenerate solution. In chapter four, we first reformulate the generalized linear complementarityproblem as a smoothing system of equations via smoothing function, based on these,a non-interior path following method for solving the generalized linear complemen-tarity problem is considered, and satisfying proper condition of error bound, weprove its global convergence and linear convergence. Some numerical experimentsof the method are also reported in this section.