A preconditioned third-order implicit-explicit algorithm with a difference of varying convex functions and extrapolation

Kelin Wu; Hongpeng Sun

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arXiv · 2509.09391

A preconditioned third-order implicit-explicit algorithm with a difference of varying convex functions and extrapolation

Kelin Wu·Hongpeng Sun

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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-\L ojasiewicz (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.

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Kelin Wu, Hongpeng Sun. 2025-09-11. A preconditioned third-order implicit-explicit algorithm with a difference of varying convex functions and extrapolation. https://arxiv.org/abs/2509.09391

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