大型稀疏无约束最优化的列分划校正Cholesky因子算法

我们考虑求解无约束优化问题1引言(?)f(x),(1)其中f：D(?)R~n→R为R~n上的二次连续可微函数,且f(x)的二阶Hesse阵H(x)稀疏、正定．为了求解问题(1),我们考虑下列Newton型方法x~(k 1)=x~k-(B~k)~(-1)▽f(x~k),k=0,1,…,(2)其中B~k是和Hesse阵H(x~k)具有相同稀疏性的近似．由于Hesse阵对称,我们假定B~k对称．为了具体说明给定矩阵B的稀疏性,我们使用M来定义指标对(i,j)的集合,其

A METHOD WITH PARTITIONING COLUMN UPDATES OF CHOLESKY FACTORIZATION FOR LARGE SCALE SPARSE UNCONSTRAINED OPTIMIZATION

In this paper,a new method for solving large scale sparse uncon- strained optimization problems is proposed.This method employs an initial Cholesky factorization of the approximation Hesse and then corrects the parti- tioning column of the diagonal factor and lower triangular factor directly and successively at each step.Iterations are generated using forward and backward substitution employing the update factorizations.A self-correcting property,a q- superlinear convergence result and an r-convergence rate estimate show that this method has good local convergence properties.The numerical results show that this method can be competitive with some current used algorithms.