一类二次投影算法的扰动分析

针对变分不等式的投影算法的一大特点是需要通过将当前迭代点投影到一个闭凸集上来产生下一步迭代点,从数值计算角度求到精确的投影几乎是不可能的,因此需要考虑当投影不能求到精确解时,对算法所产生的迭代序列的收敛性有什么影响.在经典的二次投影算法框架下,对其中的投影加以扰动,证明扰动项在小范围内变化时,经扰动后的二次投影算法仍然收敛.

A Kind of Perturbation Analysis of a Double Projection Algorithm

In each projection-type algorithm for variational inequalities,one needs to compute a projection for generating the next iteration from the current iteration.Actually,computing a projection cannot be in an exact way.So it is interesting to study whether an inexact projection would influence the convergence of the iteration sequence.We show that if one adds a perturbation term to the projection in the process of generating the next iteration and if the perturbation term is small enough,then the generated ite...