Research

Research interests: mathematical optimization, data science, numerical analysis, scientific computing, machine learning, and control, with applications spanning quantum computing, biomedical science, and materials design.

Derivative-Free Optimization and Model-Based Trust-Region Methods

• A New Derivative-Free Method Using an Improved Underdetermined Quadratic Interpolation Model — SIAM Journal on Optimization, 2025.

• Derivative-Free Optimization with Transformed Objective Functions — Journal of the Operations Research Society of China, 2025.

• Privacy-Preserving Zeroth-Order Optimization (PZOO) — arXiv preprint, 2026.

• A Derivative-Free Trust-Region Method for Optimization on Ellipsoids — Journal of Physics: Conference Series, 2023.

• ReMU: Regional Minimal Updating for Model-Based Derivative-Free Optimization — Optimization Methods and Software, 2026.

• Least H^2-Norm Updating of Quadratic Interpolation Models — IMA Journal of Numerical Analysis, 2026.

• MATRO: Metric-Aware Fully Quadratic Trust Regions for Derivative-Free Optimization — arXiv preprint, 2026.

• BUP-TR: Bayesian Underdetermined Projection Trust-Region Methods — arXiv preprint, 2026.

• TOBYQA: A Trust-Region Method for Derivative-Free Optimization on Time-Varying Functions — arXiv preprint, 2026.

Optimization for AI

• Derivative-Free Structured Updates for Muon — arXiv preprint, 2026.

AI for Optimization

• Why and When Neural Networks Improve Local Approximation in Optimization — arXiv preprint, 2026.

• Privacy-Preserving Zeroth-Order Optimization (PZOO) — arXiv preprint, 2026.

• Objective Value Change and Shape-Based Accelerated Optimization for Neural-Network Approximation — arXiv preprint, 2025.

Approximation Theory and Neural-Network Approximation

• Why and When Neural Networks Improve Local Approximation in Optimization — arXiv preprint, 2026.

• Objective Value Change and Shape-Based Accelerated Optimization for Neural-Network Approximation — arXiv preprint, 2025.

• A Novel Local Analysis of Objectives Approximated by Neural Networks: L-Change — conference paper/poster, 2024.

• Model-Driven Subspaces for Large-Scale Optimization with a Local Approximation Strategy — arXiv preprint, 2025.

Subspace Methods for Large-Scale Optimization

• 2D-MoSub: A Two-Dimensional Model-Based Subspace Method for Large-Scale DFO — Optimization Methods and Software, 2026.

• Model-Driven Subspaces for Large-Scale Optimization with a Local Approximation Strategy — arXiv preprint, 2025.

Parallel Computing and Optimization

• Parallel Model-Based Derivative-Free Optimization via Rank-Two KKT Updates — arXiv preprint, 2026.

• Distributed Gradient-Regularized Newton Method: Scheduled Consensus and Global Complexity — arXiv preprint, 2026.

Numerical Methods for Multiple Solutions of PDEs

• A Spectral Levenberg-Marquardt-Deflation Method for Multiple Solutions of Semilinear Elliptic Systems — Journal of Computational and Applied Mathematics, 2025.

• An Improved Adaptive Orthogonal-Basis Deflation Method for Nonlinear Elliptic Equations — Journal of Computational Mathematics, 2025.

• Second-Order H^1-Norm Error Analysis for Time-Fractional Advection-Dispersion Equations — arXiv preprint, 2026.

Applications in Quantum Computing, Biomedical Science, and Scientific Engineering

• Public links for the quantum-computing and biomedical manuscripts will be added when their preprints become available.

• Parametric Resonant Control of Macroscopic Behaviors of Multiple Oscillators — American Control Conference, 2019.

• Simulation of Folded-Waveguide Space Traveling-Wave Tubes with Derivative-Free Mixed-Integer NEWUOA — ICCC, 2021.

• The Modeling and Optimization of a Multi-Dam System — Applied and Computational Mathematics, 2024.