二次投影算法的扰动分析

变分不等式问题已引起国内外学者和专家的广泛关注,求解变分不等式问题的算法也很多,其中,投影算法构造简洁且被研究变分不等式算法的学者深入而细致地讨论.二次投影算法是近年来针对变分不等式提出的一类新的非常有效的投影算法.对于求解变分不等式的投影算法,投影运算非常重要.因为实际计算时,投影运算常常不能精确求解,所以有必要研究这种不精确是否影响算法的收敛性.讨论二次投影算法中关键的投影运算非精确求解时的情况,证明了扰动后的二次投影算法有意义且所产生的序列仍然收敛到变分不等式的解.

Perturbation Analysis of a Double Projection Algorithm

Variational inequality problems attract extensive attention worldwide.There are many algorithms for solving variational inequality problems.Among these algorithms,projection algorithm is one with succinct progress and has been in-depth and carefully studied.At present,double projection algorithm is one of the most effective method of projection algorithms.Projection operation is very important to projective algorithm.Frequently,projection operation is unable to solve exactly.We need to study double projection algorithm with perturbation.In this paper,we prove that the double projection algorithm after perturbation is well-defined and the generated sequence converges to a solution.