Some Projection Algorithms For Finding A Common Solution Of Variational Inequalities And Fixed Point Problems

In this thesis,we mainly study how to find the common solution of variational inequalities and fixed point problem in Hilbert space.For solving the problem,we propose two projection algorithms.Firstly,a new Tseng-like extragradient algorithm is proposed to find a common solutions between the variational inequalities with a pseudomonotone and uniformly continuous mapping and the fixed point problem with a quasi-nonexpansive mapping.Each iteration of the algorithm requires only one projection to the feasible set.Under some suitable assumptions,it is proved that the sequence generated by the algorithm converges strongly to the common solution.Numerical experiments results show the effectiveness of the algorithm.Secondly,an adaptive projection algorithm is designed to find the common solution between the variational inequalities with a quasi-monotone and Lipschitz continuous mapping and the fixed point problem with a -demicontractive mapping.Each iteration of the algorithm requires only one projection to the feasible set and the constructed half-space.By using the adaptive step,it is not necessary to know the Lipschitz continuous coefficient of the variational inequality mapping.In addition,the drop direction of the projection in the second step of this algorithm is different from the previous algorithms and the third step of the algorithm uses two Mann iterations.The weak convergence theorem of the algorithm is proved under appropriate assumptions.Numerical experiments are carried out to verify the effectiveness of the algorithm.