{"ID":2841625,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.11135","arxiv_id":"2511.11135","title":"Extended-Krylov-subspace methods for trust-region and norm-regularization subproblems","abstract":"We consider an effective new method for solving trust-region and norm-regularization problems that arise as subproblems in many optimization applications. We show that the solutions to such subproblems effectively lie in a very-low-dimensional subspace as a function of their controlling parameters (trust-region radius or regularization weight). Based on this, we build a basis spanning these solutions using an efficient extended-Krylov-subspace iteration that involves a single matrix factorization. The problems within the subspace using such a basis may be solved at very low cost using effective high-order root-finding methods. This then provides an alternative to common methods using multiple factorizations or standard Krylov subspaces. We provide numerical results to illustrate the effectiveness of our TREK/NREK approach.","short_abstract":"We consider an effective new method for solving trust-region and norm-regularization problems that arise as subproblems in many optimization applications. We show that the solutions to such subproblems effectively lie in a very-low-dimensional subspace as a function of their controlling parameters (trust-region radius...","url_abs":"https://arxiv.org/abs/2511.11135","url_pdf":"https://arxiv.org/pdf/2511.11135v3","authors":"[\"Hussam Al Daas\",\"Nicholas I. M. Gould\"]","published":"2025-11-14T10:10:41Z","proceeding":"math.NA","tasks":"[\"math.NA\",\"math.OC\"]","methods":"[]","has_code":false}