The Projection-type Algorithms Research For Variational Inequalities Problems

In this dissertation,we mainly study the projection-type algorithms for variational inequalities problems.The full text is divided into four chapters.In the first chapter,we introduce the research background and basic concepts herein.In the second chapter,a projection-type algorithm for generalized variational inequalities without monotonicity is designed in Euclidean space.We assume that a multi-valued mapping is continuous,namely,inner-semicontinuous and outer-semicontinuous.Moreover,the dual variational inequality has a solution.Under weak assumptions,we establish that the sequence generated by our algorithm is globally convergent to a solution of the problem.In the third chapter,we prove well-definedness and weak convergence of the projectiontype method for solving variational inequality problems in reflexive Banach spaces,where an operator we use is strongly continuous.The method proposed by Iusem and Svaiter [A variant of Korpelevich's method for variational inequalities with a new search strategy,Optimization,1997,42: 309-321] for solving variational inequalities in Euclidean spaces is extended to Banach spaces.In the last chapter,we give the conclusion and the prospect,illustrating the main work and innovations of this dissertation and further research prospects.