单调变分不等式问题的惯性松弛投影算法

Inertial Relaxed Projection Algorithm for Monotone Variational Inequality Problems

在Hilbert空间中研究单调变分不等式问题的惯性松弛投影算法.在该算法的每一次迭代中,只需要向特殊结构的半空间进行2次投影.另外,采取一定的线搜索条件,在单调和Lipschitz连续且Lipschitz系数大小未知的假设下,证明该算法所产生的序列强收敛到变分不等式的解.

In this paper,the inertial relaxed projection algorithm for variational inequality problems is studied in Hilbert space.In each iteration of the algorithm,only two projections are required for the semispace of the special structure.In addition,taking certain line search conditions,under the assumption that monotonic and Lipschitz are continuous and the size of the Lipschitz coefficient is unknown,it is proved that the sequence generated by the algorithm strongly converges to the solution of the variational inequality.