P. Xie and S. M. Wild, "ReMU: Regional Minimal Updating for Model-Based Derivative-Free Optimization", 2025
[Link]

P. Xie and Y.-x. Yuan, "A new derivative-free method using an improved under-determined quadratic interpolation model", 2025
SIAM Journal on Optimization, Vol. 35, Iss. 2, 1110-1133, (2025) [Link]

P. Xie and Y.-x. Yuan, "Least H2 norm updating of quadratic interpolation models for derivative-free trust-region algorithms", 2025
IMA Journal of Numerical Analysis, drae106. 03 [Link]

P. Xie, "Sufficient conditions for distance reduction between the minimizers of non-convex quadratic functions in the trust region", 2025
Journal of Computational and Applied Mathematics, [Link]

P. Xie and Y.-x. Yuan, "A new two-dimensional model-based subspace method for large-scale unconstrained derivative-free optimization: 2D-MoSub"
[Link]

K. J. Dzahini, S. M. Wild, P. Xie, "Optimization approaches for solving inverse problems must account for uncertainty in both data and downstream decisions", 2025
Position paper, Inverse Methods for Complex Systems under Uncertainty Workshop
Sponsored by the U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research [Link]

L. Li, P. Xie (Corresponding author), L. Zhang, "A novel numerical method tailored for unconstrained optimization problems", 2025
[Link]

L. Li, Y. Zhou, P. Xie (Corresponding author), H. Li, A spectral Levenberg-Marquardt-Deflation method for multiple solutions of semilinear elliptic systems, 2025
[Link]

Y. Ye, L. Li, P. Xie, and H. 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 (accepted) [Link]

P. Xie and Y.-x. Yuan, "Derivative-Free Optimization with Transformed Objective Functions and the Algorithm Based on the Least Frobenius Norm Updating Quadratic Model", 2024
Journal of the Operations Research Society of China [Link]

P. Xie and Y.-x. Yuan, "A derivative-free optimization algorithm combining line-search and trust-region techniques", 2023
Chinese Annals of Mathematics, Series B 44(5), 719–734, 2023 [Link]

P. Xie, "The Modeling and Optimization of a Multi-dam System", 2024
Applied and Computational Mathematics, 13(5), 140-152 [Link]

P. Xie, "A derivative-free trust-region method for optimization on the ellipsoid", 2023
Journal of Physics: Conference Series, 2620: 012007 [Link]

P. Xie and M. Tao, "Parametric resonant control of macroscopic behaviors of multiple oscillators"
2019 American Control Conference (ACC), 2019, pp. 1898–1905. [Link]