A preconditioned third-order implicit-explicit algorithm with a difference of varying convex functions and extrapolation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909794083799040 |
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| author | Wu, Kelin Sun, Hongpeng |
| author_facet | Wu, Kelin Sun, Hongpeng |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_09391 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A preconditioned third-order implicit-explicit algorithm with a difference of varying convex functions and extrapolation Wu, Kelin Sun, Hongpeng Optimization and Control Numerical Analysis 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. |
| title | A preconditioned third-order implicit-explicit algorithm with a difference of varying convex functions and extrapolation |
| topic | Optimization and Control Numerical Analysis |
| url | https://arxiv.org/abs/2509.09391 |