Partitioning group correction Cholesky techniques for large scale sparse unconstrained optimization

This paper studies a successive partitioning group correction Cholesky algorithm and its modified algorithm for solving large scale sparse unconstrained optimization problems. These methods employ an initial Cholesky factorization of their approximation Hessians and then correct the partitioning group(s) of their 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 the two methods both have good local convergence properties. The numerical results show that the two methods, especially the modified algorithm may be competitive with some current used algorithms.