解伪单调变分不等式的一种修正投影算法

摘要

Malitsky and Semenov(2014) presented a projection method for solving pseudo-monotone variational inequality in a Hilbert space.By this method,it only needs to compute one value of the underlying mapping and one projection onto the feasible set per iteration.In this paper,a new projection method derived from modifying its descent direction is presented for solving variational inequality.Under the same assumption,the weak convergence of the generated sequence is proved.%Malitsky和Semenov(2014)提出了一种解Hilbert空间中伪单调变分不等式的投影算法.在每次迭代中,该算法仅需计算一次映射值与一次向可行集的投影.本文修正了该算法的下降方向,从而给出了一种解变分不等式的新的投影算法.在相同的假设条件下证明了生成序列的弱收敛性.