非单调型变分不等式问题的新双投影算法

New Double Projection Algorithms for Non-monotone Variational Inequality Problems

投影算法作为一种求解变分不等式的简洁方法,常常要求所涉及的映射具有某种单调性,文献(M. Ye,Y. He. Computational Optimization and Applications,2015,60(1):141-150.)将双投影算法的标准单调性假设,用一个对偶变分不等式的解集非空的假设来替代,提出了一种新的算法,并建立了其全局收敛性.在此基础上,选取不同的超平面,提出新的算法.在对偶变分不等式问题的解集非空的假设下,建立其全局收敛性,并给出数值实验结果.

As an effective method to solve variational inequalities,the projection algorithm usually requires that the underlying mapping satisfies some monotone-type conditions.Recently,(M.Ye,Y.He.Computational Optimization and Applications,2015,60(1):141-150.)uses the assumption that the solution set of the dual variational inequality problem is nonempty to replace the standard monotonicity assumption of the underlying mapping,gives a double projection algorithm,and establishes its global convergence.In this paper,we propose new algorithms with a strategy for selecting new hyperplanes.Under the same condition as Ye’s,that is,the solution set of the dual variational inequality problem is nonempty,we prove the global convergence of the method.Numerical experiment results are reported.