Optimization plays a central role in many scientific and engineering applications. My research investigates mathematical optimization techniques, including semidefinite programming and numerical optimization methods, for the design and analysis of complex systems. Current work focuses on optimizing spectral properties of photonic crystals and developing computational frameworks for large-scale optimization problems.
Research Topics
• Semidefinite Programming (SDP)
• Convex Optimization
• Numerical Optimization
• Computational Optimization Methods
• Spectral Optimization
• Band-Gap Optimization
Current Applications
• Design and optimization of topological photonic crystals
• Shared spectral band-gap optimization
• Optimization of wave propagation in photonic structures
• Large-scale scientific computing and numerical simulations
Research Methods
• Finite Element Methods (FEM)
• Finite Difference Methods (FDM)
• Spectral Theory
• Scientific Computing
• High Performance Computing (HPC)
Software and Computational Tools
• MATLAB
• CVX
• MOSEK
• SDPT3
• Gurobi
Research Goal
To develop efficient optimization frameworks for the design and analysis of complex photonic and engineering systems through mathematical modeling, numerical methods, and scientific computing.