A Stepsize For GLP Projection Method

Variational inequality problems, with wide practicability, are a class of relatively important problems in some fields of modern mathematics. Include as special cases, d-ifferentiable constrained optimization and complementarity problems, can be solved as variational inequality problems. Among available algorithms, the projection method pro-posed by Goldstein and Levitin and Polyak plays an important role, for its simplicity. The thesis mainly studies a new step size of the projection method for asymmetric strongly monotone variational inequality problems and is divided into three chapters.The first chapter is a brief introduction to variational inequality problems, which includes their values and present research status, and gives some basic notations and some proofs of the corresponding equivalent forms.The second chapter describes the framework of the projection method, and on the base of the self-adaptive step size gives our new algorithm. Its global convergence is also proved.The third chapter gives the preliminary numerical tests, thus indicates the practica-bility and superiority of the step size proposed in this thesis.