Partitioning group correction Cholesky techniques for large scale sparse unconstrained optimization (Q858748)

The authors consider the unconstrained minimization problem of the form \[ \min f(x)\text{ subject to }x\in\mathbb{R}^n, \] where \(f:\mathbb{R}^n\to \mathbb{R}^1\) is a twice continuously differentiable function with a sparse Hessian. A successive partitioning group correction Cholesky algorithm and its modification are proposed for solving such optimization problem. A self-correcting property, a \(q\)-superlinear convergence and an \(r\)-convergence are proved. The authors report on a good computational experience with the proposed algorithms in the concluding parts of the paper, in which results of solving large test examples \((n=1000)\) as well as some comparisons with other methods are provided.