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

(* 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 New Derivative-Free Method Using an Improved 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 Distance Reduction Between the Minimizers of Nonconvex Quadratic Functions in the Trust Region” 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: 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” 2025 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” 2025 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): 693–708 [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

• Wei Hu, P. Xie*, Ya-xiang Yuan, and Li Zhang, “MATRO: Metric-Aware Fully Quadratic Trust Regions for Derivative-Free Optimization” 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*, “Privacy-Preserving Black-Box Optimization (PBBO): Theory and the Model-Based Algorithm DFOp” 2025 [Link]

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

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