一类不精确拟牛顿型算法的局部收敛性分析

Research of Convergence Analysis on a Class of In-exact Quasi-Newton Methods

为了求解Hilbert空间中算子方程或minimax问题,构造了一类无穷维空间中的不精确拟牛顿算法,并考虑了其线性收敛性和超线性收敛性,是对有限维空间中不精确拟牛顿法的推广.当迭代算子由Broyden修正给出时,在一定的假设条件下,得到了不精确Broyden方法的线性收敛性和超线性收敛性.这为使用不精确拟牛顿法结合投影法求解算子方程做好了准备.

In order to solve operator equations and minimax problems in Hilber space, a class of In-exact Quasi-Newton method are considered which does not need the computation of the second derivative. Under certain assumotions, linear and super linear convergence rate are obtained for Broyden In-exact Quasi-Newton method. It is a preparation for solving operator equations combined with the projection method.