郑仕欣

郑仕欣

Postdoc Associate, Department of Mathematics

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A list of all the posts and pages found on the site. For you robots out there, there is an XML version available for digesting as well.

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publications

Riemannian Langevin Monte Carlo schemes for sampling PSD matrices with fixed rank

Published in arXiv preprint, 2023

Constructs Langevin Monte Carlo schemes for sampling Gibbs measures on the manifold of PSD fixed-rank matrices in embedded and quotient (Bures–Wasserstein) geometries, with explicit manifold Brownian-motion corrections.

Recommended citation: T. Yu, S. Zheng, J. Lu, G. Menon, X. Zhang. (2023). "Riemannian Langevin Monte Carlo schemes for sampling PSD matrices with fixed rank." arXiv:2309.04072.
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On the convergence of orthogonalization-free conjugate gradient method for extreme eigenvalues of Hermitian matrices: a Riemannian optimization interpretation

Published in Journal of Computational and Applied Mathematics, 451:116053, 2024

Proves convergence of orthogonalization-free conjugate gradient for extreme eigenpairs of Hermitian matrices via a Riemannian optimization interpretation, with benchmarks against LOBPCG and coordinate-descent solvers. arXiv:2302.04974

Recommended citation: S. Zheng, H. Yang, X. Zhang. (2024). "On the convergence of orthogonalization-free conjugate gradient method for extreme eigenvalues of Hermitian matrices: a Riemannian optimization interpretation." Journal of Computational and Applied Mathematics, 451:116053.
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Riemannian optimization using three different metrics for Hermitian PSD fixed-rank constraints

Published in Computational Optimization and Applications, 91(3):1135–1184, 2025

Compares embedded-geometry, Burer–Monteiro, and quotient-metric formulations of optimization over Hermitian PSD fixed-rank matrices, with Riemannian CG and L-BFGS solvers and applications to matrix completion, phase retrieval, and interferometry. arXiv:2204.07830

Recommended citation: S. Zheng, W. Huang, B. Vandereycken, X. Zhang. (2025). "Riemannian optimization using three different metrics for Hermitian PSD fixed-rank constraints." Computational Optimization and Applications, 91(3):1135–1184.
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Global Convergence and Error Propagation in Neural Gradient Flows: A Riemannian Optimization Framework

Published in arXiv preprint, 2026

Reformulates minimizing-movement steps of energy minimization as Riemannian gradient flow on a neural increment manifold, proving exponential local convergence and O(δ) global function-space error propagation for Gauss–Newton-preconditioned training.

Recommended citation: S. Zheng, Y. Wang, H. Yang. (2026). "Global Convergence and Error Propagation in Neural Gradient Flows: A Riemannian Optimization Framework." arXiv:2605.27779.
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Global convergence of an efficient splitting method for the defocusing Gross–Pitaevskii ground state problem

Published in arXiv preprint, 2026

Proposes two Davis–Yin three-operator splitting schemes for the defocusing Gross–Pitaevskii ground state whose every iteration inverts only a shifted Laplacian (or a shifted Laplacian plus the separable part of the potential), and proves, for monotone discrete Laplacians, global convergence to the unique positive discrete ground state from any positive normalized initial vector at any constant step size below an explicit threshold; 3D tests with up to 9993 unknowns run on a single GPU.

Recommended citation: J. Li, S. Zheng, X. Zhang. (2026). "Global convergence of an efficient splitting method for the defocusing Gross–Pitaevskii ground state problem." arXiv:2609.13509.
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