Publications

20 papers and preprints. Grouped by research direction; * denotes lead / corresponding author. Page counts are shown where available.

Higher-Order Optimization & Sum-of-Squares

  1. C. Cartis, W. Zhu*. Cubic-Quartic Regularization Models for Solving Polynomial Subproblems in Third-Order Tensor Methods. Mathematical Programming, 2025. 53 pp Leslie Fox Prize (2nd), 2025 journalarXiv
  2. C. Cartis, W. Zhu*. Second-Order Methods for Quartically-Regularised Cubic Polynomials, with Applications to High-Order Tensor Methods. Mathematical Programming, 2025. 47 pp journalarXiv
  3. C. Cartis, W. Zhu*. Global Optimality Characterizations and Algorithms for Minimizing Quartically-Regularized Third-Order Taylor Polynomials. Mathematics of Computation, 2026. 32 pp arXiv
  4. C. Cartis, R. Hauser, Y. Liu, K. Welzel, W. Zhu. Efficient Implementation of Third-Order Tensor Methods with Adaptive Regularization for Unconstrained Optimization. Mathematical Programming Computation, 2026. 72 pp journalarXiv
  5. W. Zhu*, C. Cartis. Sufficiently Regularized Nonnegative Quartic Polynomials are Sum-of-Squares. 38 pp Under review arXiv
  6. W. Zhu*, C. Cartis. Global Convergence of High-Order Regularization Methods with Sums-of-Squares Taylor Models. SIAM Journal on Optimization, 2026. 24 pp Under review arXiv
  7. Y. Cai, W. Zhu, C. Cartis, G. Zardini. A Globally Convergent Third-Order Newton Method via Unified Semidefinite Programming Subproblems. 27 pp Under review arXiv
  8. W. Zhu*, H. Chen, G. Zhou. A Homogeneous Tensor Framework for High-Order Trust-Region and Spherical Polynomial Optimization. In prep., submitting 3Q 2026
  9. W. Zhu, C. Cartis. Quartic Polynomial Sub-Problem Solutions in Tensor Methods for Nonconvex Optimization. NeurIPS Workshop (Spotlight), 2022. 8 pp link
  10. C. Cartis, T. Lyons, B. Walker, W. Zhu. Certified Global Optimization via Higher-Order Lipschitz Branch-and-Bound with Local Sum-of-Squares Certificates. In preparation

Machine Learning & AI

  1. K. Li, W. Zhu, S. Liu. SoS1: O1- and R1-Like Reasoning LLMs are Sum-of-Squares Solvers. 16 pp Under review arXiv
  2. C. Wang, Z. Huang, Z. Li, W. Zhu. Recover Cell Tensor: Diffusion-Equivalent Tensor Completion for Fluorescence Microscopy Imaging. ICLR, 2026. 30 pp link
  3. C. Wang, Z. Li, W. Zhu, Z. Huang, X. Xiu, Z. Zhao, J. Tanner, H. Yan. Volume Tells: Dual Cycle-Consistent Diffusion for 3D Fluorescence Microscopy De-noising and Super-Resolution. IEEE TPAMI, 2026. 33 pp Under review
  4. W. Zhu* et al. Neural Sum-of-Squares: Scalable Reduced SOS Certificates via Propose-and-Verify. In preparation
  5. J. Zheng, W. Zhu, et al. CaliPPer: A Bayesian Recalibration Framework for Quantifying and Improving AI Model Performance (binding prediction). In preparation
  6. C. Wang, R. Xu, W. Zhu, J. Yang. Limited-Data SAR ATR Causal Method via Dual-Invariance Intervention. IEEE Transactions on Geoscience & Remote Sensing, 2024. 63 pp journal

Computational Finance, Risk & Operations Research

  1. C. Liu, W. Zhu. Newsvendor Conditional Value-at-Risk Minimization: A Feature-Based Approach under Adaptive Data Selection. European Journal of Operational Research, 2024. 17 pp journalarXiv
  2. C. Liu, W. Zhu. Dynamic Periodic Aggregation Sampling for Tail-Risk Data. In preparation

Numerical Analysis

  1. W. Zhu*, Y. Nakatsukasa. Convergence and Near-Optimal Sampling in Multivariate Irregular Domains via Vandermonde with Arnoldi. IMA Journal of Numerical Analysis, 2025. 35 pp journalarXiv
  2. H. Chen, W. Zhu, C. Cartis. Tensor-based Dinkelbach Method for Computing Generalized Tensor Eigenvalues and its Applications. Applied Numerical Mathematics, 2026. 29 pp journalarXiv