Publications

23 manuscripts, publications and preprints: 11 published or accepted, 6 under review or revision, 6 manuscripts available below.

Some papers list authors in alphabetical order. * denotes lead / corresponding author / author with major contribution.

Counts exclude the doctoral thesis, manuscripts in preparation and work in progress. Page counts may change for unpublished manuscripts.

Doctoral thesis

  1. K. W. Zhu. Tensor Methods for Nonconvex Optimization. D.Phil. thesis, University of Oxford (2026). Supervisor: Coralia Cartis. 194 pp. (including front matter). thesisORA

Higher-order optimization and sums of squares

  1. C. Cartis and W. Zhu*. Cubic-quartic regularization models for solving polynomial subproblems in third-order tensor methods. Mathematical Programming 217, 167–219 (2026). Leslie Fox Prize (Second Prize), 2025. 53 pp. journalarXiv
  2. C. Cartis and W. Zhu*. Second-order methods for quartically-regularised cubic polynomials, with applications to high-order tensor methods. Mathematical Programming 215, 669–715 (2026). 47 pp. journalarXiv
  3. C. Cartis and W. Zhu*. Global optimality characterizations and algorithms for minimizing quartically-regularized third-order Taylor polynomials. Mathematics of Computation (2026); arXiv:2504.20259. 32 pp. arXiv
  4. C. Cartis, R. Hauser, Y. Liu, K. Welzel and W. Zhu. Efficient implementation of third-order tensor methods with adaptive regularization for unconstrained optimization. Mathematical Programming Computation 18, 877–948 (2026). 72 pp. journalarXiv
  5. W. Zhu* and C. Cartis. Sufficiently regularized nonnegative quartic polynomials are sums-of-squares. arXiv:2601.20418 (2026). Under review, Mathematical Programming. 38 pp. arXiv
  6. W. Zhu* and C. Cartis. Global convergence of high-order regularization methods with sums-of-squares Taylor models. arXiv:2404.03035. Minor revision, SIAM Journal on Optimization (2026). 24 pp. arXiv
  7. Y. Cai, W. Zhu, C. Cartis and G. Zardini. A globally convergent third-order Newton method via unified semidefinite programming subproblems. arXiv:2603.09682 (2026). Under review. 27 pp. arXiv
  8. W. Zhu*, H. Chen and G. Zhou. A homogeneous tensor framework for high-order trust-region and spherical polynomial optimization. arXiv:2607.24046 (2026). Under review, IMA Journal of Numerical Analysis. 33 pp. arXiv
  9. W. Zhu* and P. Nie. Sum-of-Squares and Non-Sum-of-Squares Regimes for the Toeplitz Böttcher–Wenzel Form. arXiv:2610.08980v3 (updated 22 October 2026). Under review, Linear Algebra and its Applications. 26 pp. arXiv
  10. W. Zhu and C. Cartis. Quartic polynomial sub-problem solutions in tensor methods for nonconvex optimization. NeurIPS 2022 Workshop on Optimization for Machine Learning (Spotlight). 8 pp. paper

Numerical analysis, Tensor rank and algebraic geometry

  1. W. Zhu* and Y. Nakatsukasa. Convergence and near-optimal sampling for multivariate function approximations in irregular domains via Vandermonde with Arnoldi. IMA Journal of Numerical Analysis 46(4), 2072–2106 (2026; first published online 2025). 35 pp. journalarXiv
  2. H. Chen, W. Zhu and C. Cartis. Tensor-based Dinkelbach method for computing generalized tensor eigenvalues and its applications. Applied Numerical Mathematics (2026). 29 pp. journalarXiv
  3. W. Zhu* and P. Nie. A Deterministic Algorithm for Eigenvalue Separation in Tridiagonal Matrices. Manuscript, November 2026; not yet on arXiv. 27 pp. sketch of proofmanuscriptposter
  4. W. Zhu*, K. Zou and P. Nie. Two Vertices Certify a Whole Interval of Nonsingular Sign-Regular Matrices. Manuscript, November 2026; not yet on arXiv. 19 pp. sketch of proofmanuscript
  5. W. Zhu*, Q. Chen and P. Nie. Asymptotic Tensor-Rank Sublevels Need Not Be Irreducible. Manuscript, November 2026; not yet on arXiv. 16 pp. sketch of proofmanuscript
  6. W. Zhu* and P. Nie. Secant Varieties of Segre Products Need Not Be Cohen–Macaulay. Manuscript, November 2026; not yet on arXiv. 42 pp. sketch of proofmanuscript
  7. W. Zhu*, C. Liu, K. Zou and P. Nie. The Entropy Law for the Asymptotic Subrank of Dicke Tensors. Manuscript, November 2026; not yet on arXiv. 13 pp. sketch of proofmanuscript
  8. W. Zhu* and P. Nie. The Exact Partially Symmetric Rank of Products of W-States. Manuscript, November 2026; not yet on arXiv. 8 pp. sketch of proofmanuscript

Machine Learning, AI and Applications

  1. W. Zhu* and C. Cartis. Learning regularization-aware sum-of-squares certificates. WiML Workshop at NeurIPS 2026, Paris (accepted).
  2. K. Li, W. Zhu, C. Cartis, T. Ji and S. Liu. SoS1: O1- and R1-like reasoning LLMs are sum-of-squares solvers. arXiv:2502.20545 (2025). Under review. 16 pp. arXiv
  3. C. Wang, Z. Huang, Z. Li and W. Zhu. Recover Cell Tensor: diffusion-equivalent tensor completion for fluorescence microscopy imaging. International Conference on Learning Representations (ICLR), 2026. 31 pp. paperarXiv
  4. C. Wang, R. Xu, Y. Huang, J. Pei, C. Huang, W. Zhu and J. Yang. Limited-data SAR ATR causal method via dual-invariance intervention. IEEE Transactions on Geoscience and Remote Sensing 63, 1–19 (2025). 19 pp. journal
  5. C. Liu and W. Zhu. Newsvendor conditional value-at-risk minimization: a feature-based approach under adaptive data selection. European Journal of Operational Research 313(2), 548–564 (2024). 17 pp. journalarXiv

Manuscripts in preparation and work in progress

  1. C. Cartis, T. Lyons, B. Walker and W. Zhu. Certified global optimization via higher-order Lipschitz branch-and-bound with local sum-of-squares certificates. Work in progress (2027).
  2. W. Zhu* et al. SoS Atlas: scalable reduced sum-of-squares certificates via propose-and-verify. Manuscript in preparation (2027). 33 pp.
  3. J. Zheng, W. Zhu et al. CaliPPer: a Bayesian recalibration framework for quantifying and improving AI model performance. Manuscript in preparation (2026). 41 pp.
  4. W. Zhu; joint work with J. Nie, L. Zhang and C. Cartis. Global Optimization of High-Order Norm-Regularized Models: SDP Tightness and Secular Root Geometry. In preparation; planned preprint release Q4 2026. 41 pp.
  5. W. Zhu and C. Cartis. SoS Exactness for Sufficiently (Even Degree) Regularized Nonnegative Polynomials. In preparation; planned preprint release Q4 2026. 25 pp.
  6. W. Zhu and C. Cartis. From Global Optimality to Reduced SOS Exactness via Radial Bregman Quotients for Nonnegative Polynomials. In preparation; planned preprint release 2027. 22 pp.
  7. W. Zhu. Losslessness and Extreme-Slack Spectral Selection for Nonconvex Quadratic-Feature Models. Single-author manuscript in preparation; planned preprint release Q1 2027. 28 pp.