{"ID":2872191,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.09391","arxiv_id":"2509.09391","title":"A preconditioned third-order implicit-explicit algorithm with a difference of varying convex functions and extrapolation","abstract":"This paper proposes a novel preconditioned implicit-explicit algorithm enhanced with the extrapolation technique for non-convex optimization problems. The algorithm employs a third-order Adams-Bashforth scheme for the nonlinear and explicit parts and a third-order backward differentiation formula for the implicit part of the gradient flow in variational functions. The proposed algorithm, akin to a generalized difference-of-convex (DC) approach, employs a changing set of convex functions in each iteration. Under the Kurdyka-Łojasiewicz (KL) properties, the global convergence of the algorithm is guaranteed, ensuring that it converges within a finite number of preconditioned iterations. Our numerical experiments, including least squares problems with SCAD regularization and the graphical Ginzburg-Landau model, demonstrate the proposed algorithm's highly efficient performance compared to conventional DC algorithms.","short_abstract":"This paper proposes a novel preconditioned implicit-explicit algorithm enhanced with the extrapolation technique for non-convex optimization problems. The algorithm employs a third-order Adams-Bashforth scheme for the nonlinear and explicit parts and a third-order backward differentiation formula for the implicit part...","url_abs":"https://arxiv.org/abs/2509.09391","url_pdf":"https://arxiv.org/pdf/2509.09391v2","authors":"[\"Kelin Wu\",\"Hongpeng Sun\"]","published":"2025-09-11T12:17:01Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.NA\"]","methods":"[]","has_code":false}