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  2026 (12)
Derivative-Free Structured Updates for Muon. Xie, P. September 2026.
Derivative-Free Structured Updates for Muon [link]Paper   doi   link   bibtex   1 download  
MpSub: A Momentum p-Dimensional Subspace Trust-Region Method for Derivative-Free Fine-Tuning of Large Language Models. Wang, Y.; Yao, H.; and Xie, P. September 2026.
MpSub: A Momentum p-Dimensional Subspace Trust-Region Method for Derivative-Free Fine-Tuning of Large Language Models [link]Paper   doi   link   bibtex  
Why and When Neural Networks Improve Local Approximation in Optimization. Bian, C.; and Xie, P. August 2026.
Why and When Neural Networks Improve Local Approximation in Optimization [link]Paper   doi   link   bibtex   1 download  
TOBYQA: A Trust-Region Method for Derivative-Free Optimization on Time-Varying Functions. Yao, H.; and Xie, P. arXiv preprint arXiv:2608.18124, August 2026. Published August 2026
TOBYQA: A Trust-Region Method for Derivative-Free Optimization on Time-Varying Functions [link]Paper   doi   link   bibtex  
ReMU: Regional Minimal Updating for Model-Based Derivative-Free Optimization. Xie, P.; and Wild, S. M. Optimization Methods and Software,1–30. 2026.
ReMU: Regional Minimal Updating for Model-Based Derivative-Free Optimization [link]Paper   doi   link   bibtex  
Least $H^2$ Norm Updating of Quadratic Interpolation Models for Derivative-Free Trust-Region Algorithms. Xie, P.; and Yuan, Y. IMA Journal of Numerical Analysis, 46(1): 21–50. 2026.
Least $H^2$ Norm Updating of Quadratic Interpolation Models for Derivative-Free Trust-Region Algorithms [link]Paper   doi   link   bibtex  
A New Two-Dimensional Model-Based Subspace Method for Large-Scale Unconstrained Derivative-Free Optimization: 2D-MoSub. Xie, P.; and Yuan, Y. Optimization Methods and Software, 41(1): 118–150. 2026.
A New Two-Dimensional Model-Based Subspace Method for Large-Scale Unconstrained Derivative-Free Optimization: 2D-MoSub [link]Paper   doi   link   bibtex  
Second-order $H^1$-norm Error Analysis for Time-Fractional Advection-Dispersion Equations Based on the Fast Averaged L1 Method. Huang, L.; Li, L.; and Xie, P. 2026.
Second-order $H^1$-norm Error Analysis for Time-Fractional Advection-Dispersion Equations Based on the Fast Averaged L1 Method [link]Paper   link   bibtex  
MATRO: Metric-Aware Fully Quadratic Trust Regions for Derivative-Free Optimization. Hu, W.; Xie, P.; Yuan, Y.; and Zhang, L. 2026.
MATRO: Metric-Aware Fully Quadratic Trust Regions for Derivative-Free Optimization [link]Paper   link   bibtex  
BUP-TR: Bayesian Underdetermined Projection Trust-Region Methods for Derivative-Free Optimization. Hu, W.; Xie, P.; Yuan, Y.; and Zhang, L. 2026.
BUP-TR: Bayesian Underdetermined Projection Trust-Region Methods for Derivative-Free Optimization [link]Paper   link   bibtex  
Distributed Gradient-Regularized Newton Method: Scheduled Consensus and $O(ε^{-1})$ Global Iteration Complexity. Hu, W.; Xie, P.; Yuan, Y.; and Zhang, L. 2026.
Distributed Gradient-Regularized Newton Method: Scheduled Consensus and $O(ε^{-1})$ Global Iteration Complexity [link]Paper   link   bibtex  
Privacy-Preserving Black-Box Optimization (PBBO): Theory and the Model-Based Algorithm DFOp. Xie, P. 2026.
Privacy-Preserving Black-Box Optimization (PBBO): Theory and the Model-Based Algorithm DFOp [link]Paper   link   bibtex  
  2025 (9)
A New Derivative-Free Method Using an Improved Underdetermined Quadratic Interpolation Model. Xie, P.; and Yuan, Y. SIAM Journal on Optimization, 35(2): 1110–1133. 2025.
A New Derivative-Free Method Using an Improved Underdetermined Quadratic Interpolation Model [link]Paper   doi   link   bibtex  
Sufficient Conditions for Error Distance Reduction in the $\ell_2$-Norm Trust Region Between Minimizers of Local Nonconvex Multivariate Quadratic Approximates. Xie, P. Journal of Computational and Applied Mathematics, 453: 116146. 2025.
Sufficient Conditions for Error Distance Reduction in the $\ell_2$-Norm Trust Region Between Minimizers of Local Nonconvex Multivariate Quadratic Approximates [link]Paper   doi   link   bibtex  
Derivative-Free Optimization with Transformed Objective Functions (DFOTO) and the Algorithm Based on the Least Frobenius Norm Updating Quadratic Model. Xie, P.; and Yuan, Y. Journal of the Operations Research Society of China, 13: 327–363. 2025.
Derivative-Free Optimization with Transformed Objective Functions (DFOTO) and the Algorithm Based on the Least Frobenius Norm Updating Quadratic Model [link]Paper   doi   link   bibtex  
A Spectral Levenberg–Marquardt-Deflation Method for Multiple Solutions of Semilinear Elliptic Systems. Li, L.; Zhou, Y.; Xie, P.; and Li, H. Journal of Computational and Applied Mathematics, 475: 116998. 2025.
A Spectral Levenberg–Marquardt-Deflation Method for Multiple Solutions of Semilinear Elliptic Systems [link]Paper   doi   link   bibtex  
An Improved Adaptive Orthogonal Basis Deflation Method for Multiple Solutions with Applications to Nonlinear Elliptic Equations in Varying Domains. Ye, Y.; Li, L.; Xie, P.; and Yu, H. Journal of Computational Mathematics, 44(3): 794–818. 2025.
An Improved Adaptive Orthogonal Basis Deflation Method for Multiple Solutions with Applications to Nonlinear Elliptic Equations in Varying Domains [link]Paper   doi   link   bibtex  
Optimization Approaches for Solving Inverse Problems Under Uncertainty. Dzahini, K. J.; Wild, S. M.; and Xie, P. Inverse Methods for Complex Systems under Uncertainty Workshop. 2025. Position paper, U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research
Optimization Approaches for Solving Inverse Problems Under Uncertainty [pdf]Paper   link   bibtex  
A Novel Numerical Method Tailored for Unconstrained Optimization Problems. Li, L.; Xie, P.; and Zhang, L. 2025.
A Novel Numerical Method Tailored for Unconstrained Optimization Problems [link]Paper   link   bibtex  
Objective Value Change and Shape-Based Accelerated Optimization for Neural Network Approximation. Xie, P.; Zhou, Z.; and Zhou, Z. 2025.
Objective Value Change and Shape-Based Accelerated Optimization for Neural Network Approximation [link]Paper   link   bibtex  
Model-Driven Subspaces for Large-Scale Optimization with Local Approximation Strategy. He, Y.; and Xie, P. 2025.
Model-Driven Subspaces for Large-Scale Optimization with Local Approximation Strategy [link]Paper   link   bibtex  
  2024 (7)
The Modeling and Optimization of a Multi-Dam System. Xie, P. Applied and Computational Mathematics, 13(5): 140–152. 2024.
The Modeling and Optimization of a Multi-Dam System [link]Paper   doi   link   bibtex  
On the Relationship Between $Λ$-Poisedness in Derivative-Free Optimization and Outliers in Local Outlier Factor. Xie, P. 2024.
On the Relationship Between $Λ$-Poisedness in Derivative-Free Optimization and Outliers in Local Outlier Factor [link]Paper   link   bibtex  
Barycenter of the Weight-Coefficient Region of Least-Weighted $H^2$ Norm Updating Quadratic Models with Vanishing Trust-Region Radius. Xie, P.; and Wild, S. M. 2024. SIAM Northern and Central California Sectional Conference (NCC24), Early Career Travel Award
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A Novel Local Analysis of Objectives Approximated by Neural Networks: L-Change. Xie, P.; and others 2024. International Conference on Mathematical Theory of Deep Learning (MTDL)
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A Low-Computation-Cost Cubic-Regularized Quasi-Newton Method for Distributed Optimization: LC3RQN. Hu, W.; Xie, P.; Zhang, L.; and Yuan, Y. 2024.
A Low-Computation-Cost Cubic-Regularized Quasi-Newton Method for Distributed Optimization: LC3RQN [pdf]Paper   link   bibtex   29 downloads  
An Efficient Derivative-Free Method for Finding Multiple Solutions. Xie, P. 2024. Manuscript
link   bibtex  
A Note on the Invariant Distribution of a Stochastic Dynamical System. Xie, P. 2024.
A Note on the Invariant Distribution of a Stochastic Dynamical System [link]Paper   doi   link   bibtex  
  2023 (2)
A Derivative-Free Optimization Algorithm Combining Line-Search and Trust-Region Techniques. Xie, P.; and Yuan, Y. Chinese Annals of Mathematics, Series B, 44(5): 693–708. 2023.
A Derivative-Free Optimization Algorithm Combining Line-Search and Trust-Region Techniques [link]Paper   doi   link   bibtex   5 downloads  
A Derivative-Free Trust-Region Method for Optimization on the Ellipsoid. Xie, P. Journal of Physics: Conference Series, 2620: 012007. 2023. Presented at the 2023 International Conference on Advances in Computer Science and Engineering Technology
A Derivative-Free Trust-Region Method for Optimization on the Ellipsoid [link]Paper   doi   link   bibtex   4 downloads  
  2021 (1)
Simulation of Interaction of Folded Waveguide Space Traveling Wave Tubes with Derivative-Free Mixed-Integer-Based NEWUOA Algorithm. Li, S.; Xie, P.; Zhou, Z.; and others In 2021 7th International Conference on Computer and Communications (ICCC), pages 1215–1219, 2021.
Simulation of Interaction of Folded Waveguide Space Traveling Wave Tubes with Derivative-Free Mixed-Integer-Based NEWUOA Algorithm [link]Paper   doi   link   bibtex  
  2019 (1)
Parametric Resonant Control of Macroscopic Behaviors of Multiple Oscillators. Xie, P.; and Tao, M. In 2019 American Control Conference (ACC), pages 1898–1905, 2019.
Parametric Resonant Control of Macroscopic Behaviors of Multiple Oscillators [link]Paper   doi   link   bibtex   5 downloads