求解双层集值混合变分不等式的惯性外梯度算法

INERTIAL EXTRAGRADIENT ALGORITHMS FOR SOLVING BILEVEL MULTIVALUED MIXED VARIATIONAL INEQUALITIES

本文在Tseng外梯度算法的基础上,引入了一种求解双层集值混合变分不等式的惯性外梯度算法.该算法的步长是非单调自适应的.结合惯性加速技巧.在集值映射是单调且Lipschitz连续的假设下,证明了该算法所产生的序列强收敛到双层集值混合变分不等式的解.进行的数值实验表明惯性外梯度算法优于-些已有的算法.

In this paper,based on Tseng's extragradient algorithm,inertial extragradient algorithm for solving bilevel multivalued mixed variational inequalities is presented.The step sizes of the proposed algorithm are adaptive and non-monotonic.Combined with the inertial acceleration techniques,it is proved that the sequence generated by the algorithm converges strongly to solution of the bilevel multivalued mixed variational inequalities,under the assumption that the multi-valued mapping is monotone and Lipschitz continuous.Some numerical experiments have showed that the inertial extragradient algorithm has a competitive advantage over some existing algorithms.