An Improved Subgradient Extragradient Algorithm For Generalized Variational Inequality

In this dissertation,some existing projection algorithms for solving generalized variational inequalities are briefly analyzed and studied,and their advantages and disadvantages are introduced respectively.On the basis of Malitsky and Semenov’s modified subgradient extragradient algorithm for solving single-valued variational inequalities,combined with the requirements of generalized variational inequalities,the original algorithm for solving single-valued variational inequalities is extended to generalized variational inequalities.Compared with some algorithms that require auxiliary programs to ensure iteration points on the feasible set,our new algorithm abandons the auxiliary programs.However,at the same time,our algorithm has a stronger requirement for continuity,requiring Lipschitz continuity of functions on the feasible set.Compared with Malitsky and Semenov’s algorithms that must know the Lipschitz constant,when the Lipschitz constant of the mapping is difficult to determine,the adaptive step size is added in our algorithm,so that the new algorithm does not need to know the Lipschitz constant.Then,in order to speed up the algorithm,we add inertia term to the algorithm.It is proved that the iterative sequence generated by this algorithm converges under the proper assumption of the cost function.Finally,we prove the efficiency of our algorithm through some numerical experiments.