Algorithms For Common Solutions Of Variational Inequality And Fixed Point Problems

In this thesis,we present a modified inertial subgradient extra-gradient algorithm for finding a common element of the solution set of variational inequality problems and the fixed point set of a nonexpansive mapping,and a modified projection and contraction algorithm for finding a common element of the solution set of variational inequality problems and the fixed point set of a demicontractive mapping.Under suitable assumptions,we establish the weak convergence theorem of the modified inertial subgradient extragradient algorithm and the strong convergence theorem of the modified projection and contraction algorithm.The thesis is divided into three chapters,the main content of each chapter is as followsIn chapter 1,we introduce the research background,current situation of variational inequality problems and fixed point problems,and the main content of this thesis.In chapter 2,we present a modified inertial subgradient extragradient al-gorithm for finding a common element of the fixed points set of a nonexpansive mapping and the solution set of the variational inequality problem for a monotone.lipschitz continuous mapping.The algorithm is a combination of the general sub-gradient extragradient algorithm and the inertial algorithm,which can speed up the convergence speed of the algorithm.Under suitable assumptions,we establish the weak convergence theorem of the modified inertial subgradient extragradient algorithm.We give the numerical experiment to show that our algorithm requires fewer iteration steps and takes less time to run than Algorithm 6.1 in[9]under the same precision conditionsIn chapter 3,we present a modified projection and contraction algorithm for finding a common element of the solution set of variational inequality problems and the fixed point set of a demicontractive mapping.Under suitable assump-tions,we establish the strong convergence theorem of the modified projection and contraction algorithm,the weak convergence results of the projection and contraction algorithm proposed by Dong[23]are generalized,and we weaken the nonexpansive mapping T in[23]to a demicontractive mapping.Finally,we give the corresponding numerical experiment.