Selected publications and preprints are listed below. See the longer BibBase list at the end for additional details.

Research Highlights — Read about the significance and my contributions behind six papers on derivative-free optimization.

(* denotes corresponding author)

Selected Publications

• P. Xie* and Stefan M. Wild, “ReMU: Regional Minimal Updating for Model-Based Derivative-Free Optimization” 2026 Optimization Methods and Software, 1–30 [Link]

• P. Xie* and Ya-xiang Yuan, “A Derivative-Free Method Using a New Underdetermined Quadratic Interpolation Model” 2025 SIAM Journal on Optimization, 35(2): 1110–1133 [Link]

• P. Xie* and Ya-xiang Yuan, “Least H^2 Norm Updating of Quadratic Interpolation Models for Derivative-Free Trust-Region Algorithms” 2026 IMA Journal of Numerical Analysis, 46(1): 21–50 [Link]

• P. Xie*, “Sufficient Conditions for Error Distance Reduction in the ℓ²-Norm Trust Region Between Minimizers of Local Nonconvex Multivariate Quadratic Approximates” 2025 Journal of Computational and Applied Mathematics, 453: 116146 [Link]

• P. Xie* and Ya-xiang Yuan, “A New Two-Dimensional Model-Based Subspace Method for Large-Scale Unconstrained Derivative-Free Optimization: 2D-MoSub” 2026 Optimization Methods and Software, 41(1): 118–150 [Link]

• P. Xie* and Ya-xiang Yuan, “Derivative-Free Optimization with Transformed Objective Functions and the Algorithm Based on the Least Frobenius Norm Updating Quadratic Model” 2025 Journal of the Operations Research Society of China, 13(2): 327–363 [Link]

• Lin Li, Yuheng Zhou, P. Xie*, and Huiyuan Li, “A Spectral Levenberg-Marquardt-Deflation Method for Multiple Solutions of Semilinear Elliptic Systems” — 2026 Journal of Computational and Applied Mathematics, 475: 116998 [Link]

• Yangyi Ye, Lin Li, P. Xie, and Haijun Yu, “An Improved Adaptive Orthogonal Basis Deflation Method for Multiple Solutions with Applications to Nonlinear Elliptic Equations in Varying Domains” — 2026 Journal of Computational Mathematics, 44(3): 794–818 [Link]

• Kwassi J. Dzahini, Stefan M. Wild, and P. Xie, “Optimization Approaches for Solving Inverse Problems under Uncertainty” 2025 Inverse Methods for Complex Systems under Uncertainty Workshop, U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research [Link]

• P. Xie*, “Ph.D. Thesis: Algorithms and Theory of Derivative-Free Optimization” 2024 [Full English Version] [Full Version] [Need to access]

• P. Xie* and Ya-xiang Yuan, “A Derivative-Free Optimization Algorithm Combining Line-Search and Trust-Region Techniques” 2023 Chinese Annals of Mathematics, Series B, 44(5): 719–734 [Link]

• P. Xie*, “The Modeling and Optimization of a Multi-Dam System” 2024 Applied and Computational Mathematics, 13(5): 140–152 [Link]

• P. Xie* and Molei Tao, “Parametric Resonant Control of Macroscopic Behaviors of Multiple Oscillators” 2019 American Control Conference (ACC), pp. 1898–1905 [Link]

• P. Xie*, “A Derivative-Free Trust-Region Method for Optimization on the Ellipsoid” 2023 Journal of Physics: Conference Series, 2620: 012007 [Link]

Selected Preprints and Manuscripts

• P. Xie* and Lucas Cabral, “A block reduction for stationary covariances of linear stochastic second-order systems”. Preprint, 2026. [DOI / Preprint]

• P. Xie* and Lucas Cabral, “Poisedness and local outlier factors in derivative-free trust-region optimization”. Preprint, 2026. [DOI / Preprint]

• Churui Wang and P. Xie*, “Hybrid Neural Network Training with Two-Dimensional Model-Based Subspace Search”. Preprint, 2026. [DOI / Preprint]

• P. Xie* and Hongzheng Yi, “Subspace Trust Region Policy Optimization with a Direct Reduced Fisher Matrix”. Preprint, 2026. [DOI / Preprint]

• Shengminjie Chen, Xiaoming Sun, P. Xie, Wenguo Yang, Zhicheng Yao, and Zijian Zhou, “A Two-Stage Variational Quantum Solver for Random-Feature PDE Discretizations”. Preprint, 2026.
  [DOI / Preprint]

• Shu Zhang and P. Xie*, “Derivative-Free Trust-Region Methods in Local Coordinates on Riemannian Manifolds”. Preprint, 2026.
  [DOI / Preprint]

• Zhixin Li, P. Xie, and Zijian Zhou, “Local Oscillation for Convolutional Neural Networks: A Reconstructed Measure for Image Classification across Three Backbone Families”. Preprint, 2026.
  [DOI / Preprint]

• Yiwen Chen and P. Xie, “Random-subspace Ellipsoidal Trust-region Methods for Derivative-free Optimization” 2026 arXiv preprint, arXiv:2610.24866 [Link] [PDF]

• P. Xie*, “Derivative-Free Structured Updates for Muon” 2026 [Link] [DOI]

• Yuyang Wang, Haoyu Yao, and P. Xie*, “MpSub: A Momentum p-Dimensional Subspace Trust-Region Method for Derivative-Free Fine-Tuning of Large Language Models” 2026 [Link] [DOI]

• Chengkuo Bian and P. Xie*, “Why and When Neural Networks Improve Local Approximation in Optimization” 2026 [Link] [DOI]

• Donghan Wu and P. Xie*, “Parallel Model-Based Derivative-Free Optimization via Rank-Two KKT Updates” 2026 [Link] [DOI]

• Haoyu Yao and P. Xie*, “TOBYQA: A Trust-Region Method for Derivative-Free Optimization on Time-Varying Functions” 2026 [Link] [DOI]

• Liangcai Huang, Lin Li*, and P. Xie*, “Second-order H¹-norm error analysis for time-fractional advection-dispersion equations based on the fast averaged L1 method” 2026 [Link]

• Wei Hu*, P. Xie, Ya-xiang Yuan, and Li Zhang, “MATRO: Metric-Aware Trust-Region Optimization with Fully Quadratic Models” 2026 [Link]

• Wei Hu, P. Xie*, Ya-xiang Yuan, and Li Zhang, “BUP-TR: Bayesian Underdetermined Projection Trust-Region Methods for Derivative-Free Optimization” 2026 [Link]

• Wei Hu*, P. Xie, Ya-xiang Yuan, and Li Zhang, “Distributed Gradient-Regularized Newton Method: Scheduled Consensus and O(ε^{-1}) Global Iteration Complexity” 2026 [Link]

• P. Xie* and Jianqing Fan, “Privacy-Preserving Zeroth-Order Optimization (PZOO): Theory and the Model-Based Algorithm DFOp”. Manuscript, 2026.
  [Earlier version: PBBO]

• Lin Li, P. Xie*, and Li Zhang, “A Novel Numerical Method Tailored for Unconstrained Optimization Problems” 2025 [Link]

• P. Xie*, Zihao Zhou, and Zijian Zhou, “Objective Value Change and Shape-Based Accelerated Optimization for Neural Network Approximation” 2025 [Link]

• Yitong He, P. Xie*, and William W. Hager, “Model-Driven Subspaces for Large-Scale Optimization with Local Approximation Strategy” 2025 [Link]

• P. Xie* and Rui Gao, “Convergence and High-Probability Complexity of Stochastic Trust-Region Methods”. Manuscript, 2025.

• P. Xie* and Rui Gao, “High-Probability Complexity Analysis of Stochastic Adaptive Cubic Regularization Algorithm”. Manuscript, 2025.

Selected Posters

• Distributed Gradient-Regularized Newton Method: Scheduled Consensus and O(ε⁻¹) Global Iteration Complexity [Link]
  Wei Hu, Pengcheng Xie, Ya-Xiang Yuan, and Li Zhang
  MOA 2026 International Workshop on Modern Optimization and Applications

• Barycenter of Weight Coefficient Region of Least Weighted H² Norm Updating Quadratic Models for Derivative-Free Optimization [Link]
  Pengcheng Xie (pxie@lbl.gov) and Stefan M. Wild (wild@lbl.gov)
  SIAM Northern and Central California Sectional Conference (NCC24), Early Career Travel Award

• A Novel Local Analysis of Objectives Approximated by Neural Network: L-Change [Link]
  Pengcheng Xie, Zihao Zhou, and Zijian Zhou
  2024 International Conference on Mathematical Theory of Deep Learning (MTDL)

• A Low Computation Cost Cubic Regularized Quasi-Newton Method for Distributed Optimization: LC3RQN [Link]
  Wei Hu, Pengcheng Xie, Ya-xiang Yuan, and Li Zhang
  2024 International Workshop on Modern Optimization and Applications

• Advanced Subspaces for Large-Scale Optimization with Local Approximation Strategy [Link]
  Yitong He and Pengcheng Xie
  The First Youth Academic Conference of the Operations Research Society of China (ORSC)

Longer List