解变分不等式问题的一种半压缩惯性投影算法

Inertial projection algorithm with demicontractive mapping for solving variational inequalities

提出了一种带有λ-半压缩映像的惯性收缩投影方法,用以寻找带有半压缩映像的不动点集与单调变分不等式解集的公共元,在Lipschitz连续及自适应步长的条件下,证明了由该算法所产生的迭代序列强收敛于某公共元。最后,用数值实验验证了该算法的有效性。

Inertial projection and contraction algorithm with λ-demicontractive mapping is proposed to find the common element of the fixed point set with a demicontractive mapping and the set of a monotone variational inequality,and it is proved that the iterative sequence generated by the algorithm is strongly converged on a common element under the condition that the algorithm is implemented with a self-adaptive step size rule and the Lipschitz continuity.Finally,the efficiency and advantages of the proposed method is verified by computational tests.