Performance of a multifrontal scheme for partially separable optimization

We consider the solution of partially separable minimization problems subject to simple bounds constraints. At each iteration, a quadratic model is used to approximate the objective function within a trust region. To minimize this model, the iterative method of conjugate gradients has usually been used. The aim of this paper is to compare the performance of a direct method, a multifrontal scheme, with the conjugate gradient method (with and without preconditioning). To assess our conclusions, a set of numerical experiments, including large dimensional problems, is presented.

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