广义Armijo步长搜索下的梯度算法的收敛特征

SOME CONVERGENCE PROPERTIES OF GRADIENT METHOD WITH GENERALIZED ARMIJO STEP SIZE RULE

:对无约束规划 (P) :minx∈Rnf(x) ,其中 ,f(x)是Rn→R1上的一阶连续可微函数 ,在去掉迭代点列 {xk}有界和广义Armijo步长搜索下 ,讨论了梯度算法的全局收敛性 ,证明了算法具有较强的收敛性质。

The convergence properties of gradient method for minimizing a continuously differentiable function f on R n with generalized Armijo step size rule are discussed assuming that the sequence {x k} of iterates is not bounded. We establish strong convergence properties of this gradient method.