约束半光滑方程组的投影牛顿类法

Projected Newton-like Methods for Solving Bound-constrained Semi-smooth Equations

给出了解决带变量有界约束的半光滑方程组问题的投影牛顿类法,该法避免了迭代点落在约束区间之外的可能,采用将每步的牛顿类方向在可行集上做投影的方法迫使迭代点始终落在可行集内,并根据具体算法步骤进行了收敛性分析.结果表明,算法具有局部超线性收敛速率,且在一定条件下可达二次收敛.

Projected Newton-like methods for solving bound-constrained semi-smooth equations are proposed.In order to generate feasible iterates,Newton-like method that is augmented by the projection onto feasible set,is introduced.It is proved that the additional projection does not affect the local super-linear convergence speed.A full proof of the local super-linear convergence results is given.