求解非单调变分不等式的一种二次投影算法

A Double Projection Algorithm for Solving Non-Monotone Variational Inequalities

投影算法是求解变分不等式问题的主要方法之一.目前,有关投影算法的研究通常需要假设映射是单调且Lipschitz连续的,然而在实际问题中,往往不满足这些假设条件.该文利用线搜索方法,提出了一种新的求解非单调变分不等式问题的二次投影算法.在一致连续假设下,证明了算法产生的迭代序列强收敛到变分不等式问题的解.数值实验结果表明了该文所提算法的有效性和优越性.

The projection algorithm is one of the main methods to solve variational inequality problems.At present,the research on projection algorithms usually requires the assumptions that the mapping is monotone and Lipschitz continuous,but in practical problems,these assumptions are often unsatisfied.A new double projection algorithm for solving non-monotone variational inequality problems was proposed with the line search method.Under the assumption that the mapping is uniformly continuous,the sequence generated by the algorithm was proved to strongly converge to the solution of the variational inequality.The numerical experiments illustrate the effectiveness and superiority of the proposed algorithm.