【摘要】 考虑了经典变分不等式的投影算法.在假设映射伪单调和利普希茨连续的条件下,给出了一种变分不等式的投影算法.所给出的算法结合梯度方法和Mann迭代,在不知道映射的利普希茨常数的前提下,证明了所提出的算法收敛到变分不等式解集中,同时也收敛到半压缩映射的不动点中.更多还原

【Abstract】 In this paper, we consider a projection algorithm for solving variational inequalities. We give a projection algorithm for solving variational inequalities involving pseudomontone and Lipschitz-type mapping.The algorithm combine extragradient method and Mann method. Without the knowledge of the Lipschitz-type constant of the mapping, it is proved that the proposed algorithm converges to the solution set of variational inequalities and to the fixed point of the demicontractive mapping.更多还原