arXiv subjects

Xinhua Shen

Publications and source records attributed to Xinhua Shen.

3 recordsLinked to original sources

arXiv2026

A boosted second-order convex splitting algorithm based on gradient flows

This paper introduces a second-order convex splitting scheme for gradient flows arising in phase-field models, based on the backward differentiation formula (BDF2) for the implicit part and the Adams-Bashforth method for the nonlinear and explicit component. The method is formulated and analyzed in finite-dimensional spaces, where energy stability plays a central role in establishing rigorous convergence properties. By leveraging the Kurdyka-Łojasiewicz framework, we prove the global convergence of the discrete trajectories generated by the scheme, even in the presence of nonsmooth energy functionals, under mild assumptions on the time-step size. The Armijo line search strategy and the classical preconditioning strategies, such as symmetric Gauss-Seidel and Jacobi, are incorporated to improve its computational efficiency. Numerical experiments confirm that the proposed method achieves computational efficiency compared to existing first-order splitting approaches and other accelerated splitting algorithms, while maintaining robustness in both smooth and nonsmooth regimes.

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arXiv2025

A preconditioned second-order convex splitting algorithm with extrapolation

Nonconvex optimization problems are widespread in modern machine learning and data science. We introduce an extrapolation strategy into a class of preconditioned second-order convex splitting algorithms for nonconvex optimization problems. The proposed algorithms combine second-order backward differentiation formulas (BDF2) with an extrapolation method. Meanwhile, the implicit-explicit scheme simplifies the subproblem through a preconditioned process. As a result, our approach solves nonconvex problems efficiently without significant computational overhead. Theoretical analysis establishes global convergence of the algorithms using Kurdyka-Łojasiewicz properties. Numerical experiments include a benchmark problem, the least squares problem with SCAD regularization, and an image segmentation problem. These results demonstrate that our algorithms are highly efficient, as they achieve reduced solution times and competitive performance.

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arXiv2023

Preconditioned Algorithm for Difference of Convex Functions with applications to Graph Ginzburg-Landau Model

In this work, we propose and study a preconditioned framework with a graphic Ginzburg-Landau functional for image segmentation and data clustering by parallel computing. Solving nonlocal models is usually challenging due to the huge computation burden. For the nonconvex and nonlocal variational functional, we propose several damped Jacobi and generalized Richardson preconditioners for the large-scale linear systems within a difference of convex functions algorithms framework. They are efficient for parallel computing with GPU and can leverage the computational cost. Our framework also provides flexible step sizes with a global convergence guarantee. Numerical experiments show the proposed algorithms are very competitive compared to the singular value decomposition based spectral method.

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