The Comparison Of Algorithms For Solving Co-coercive Variational Inequalities

This thesis studies the projection algorithms for solving co-coercive variational inequalities.First,we introduce the conceptions and properties of the projection algorithm and list three existing algorithms. Furthermore, we propose a new algorithm (algorithm 4) related with co-coercive modulus. According to numerical experiments, we compare the convergence rates of three algorithms including this new algorithm and two existing ones. We find that the selection of the co-coercive modulus has a great impact on the convergence rate of the new algorithm, which leads to uncertainty of the convergence rate. To avoid this uncertainty, we create another new algorithm (algorithm 5) which is not related with the co-coercive modulus and prove its convergence property. The advantage of this improved algorithm are to avoid the estimation of the co-coercive modulus and match its proper descent direction and correction step size. The numeri-cal results show that the improved algorithm is efficient for both linear and nonlinear variational inequality.We will provide algorithm 4, algorithm 5 and their proofs of convergence in Chap-ter 4 and Chapter 5, and the results of our experiments will be shown in Chapter 6.