My research lies at the intersection of optimization, computational modeling, and engineering decision systems. I develop mixed-integer, combinatorial, and nonconvex optimization methods for large-scale problems arising in healthcare and other complex engineered systems. A central theme of my work is the exploitation of problem structure: physical, biological, geometric, and data-driven, to design scalable algorithms with provable performance guarantees.
My research integrates mathematical programming, approximation algorithms, decomposition techniques, and quantum-inspired optimization to address computational challenges in high-dimensional decision-making. By combining methodological advances with application-driven insights, I seek to develop optimization frameworks that enable more efficient, reliable, and interpretable engineering systems.
Research Theme 1: Optimization for Radiation Therapy and Medical Physics
Radiation therapy planning in cancer treatment presents a unique class of large-scale optimization problems involving competing clinical objectives, complex physical constraints, and discrete treatment decisions. My research develops optimization frameworks for treatment planning in various radiation delivery modalities: proton therapy, intensity-modulated proton therapy (IMPT), proton minibeam therapy, and spatially fractionated radiotherapy.
Recent contributions include mixed-integer optimization models for proton minibeam aperture selection, geometry-adaptive optimization frameworks for LATTICE radiotherapy, and biologically informed planning methodologies that improve normal tissue sparing while maintaining tumor control. Through this work, I aim to advance next-generation treatment planning methods that are clinically practical, computationally scalable, and scientifically rigorous.
Research Theme 2: Mixed-Integer and Large-Scale Optimization
Many engineering and healthcare systems require decision-making under discrete constraints, limited resources, and high-dimensional design spaces. My research focuses on the development of exact and approximate optimization methods for such problems.
I am particularly interested in mixed-integer programming, combinatorial optimization, decomposition methods, convex relaxation techniques, and scalable algorithms for large-scale decision systems. By exploiting problem-specific structure, such as sparsity, hierarchy, and decomposability, I seek to develop optimization frameworks capable of solving problems that are beyond the reach of conventional approaches.
Applications include treatment planning, scheduling, resource allocation, and other engineering decision problems.
Research Theme 3: Quantum-Inspired Optimization and Emerging Computational Paradigms
As optimization problems continue to grow in complexity, new computational paradigms are needed to complement traditional algorithms. My research investigates quantum-inspired and hybrid optimization approaches for solving large-scale combinatorial and mixed-integer problems.
Current work includes quantum optimization frameworks for beam angle optimization, variational quantum methods for treatment planning, and tensor-network-based approaches for sparse optimization problems. My broader goal is to understand when quantum-inspired methods can provide practical computational advantages and how they can be integrated with classical optimization techniques to address challenging engineering applications.
Research Theme 4: Optimization Theory and Computational Modeling
Alongside application-driven research, I work on the mathematical foundations of optimization and learning. My interests include approximation algorithms, memory-efficient optimization methods, structured convex optimization, nonconvex optimization, and geometric methods for high-dimensional learning.
My previous work has contributed algorithms with provable guarantees for combinatorial optimization, clustering, and structured optimization problems. I am particularly interested in developing theoretically sound methods that bridge optimization, machine learning, and scientific computing, enabling robust decision-making in data-rich environments.
Future Research Directions
My long-term goal is to build a research program centered on structure-aware optimization for complex engineering systems. Future work will focus on three interconnected directions:
Mixed-Integer and Combinatorial Optimization for Complex Systems
Developing scalable optimization frameworks for large-scale engineering and healthcare decision problems involving discrete choices, uncertainty, and multi-level decision structures. This includes new mixed-integer formulations, decomposition methods, and approximation techniques for computationally challenging applications.
Nonconvex Optimization and Computational Modeling
Designing optimization methods that can accurately capture nonlinear system behavior arising from biological processes, physical transport models, and coupled engineering systems. Emphasis will be placed on structure-exploiting algorithms, low-memory methods, and rigorous convergence analysis.
Quantum-Inspired and Hybrid Optimization Algorithms
Developing next-generation optimization methodologies that combine mathematical programming with quantum-inspired computation, variational techniques, and advanced sampling methods. The goal is to create scalable algorithms for solving high-dimensional combinatorial problems that arise across healthcare, scientific computing, and engineering design.
By integrating optimization theory, computational modeling, and real-world applications, my research seeks to advance both the mathematical foundations of decision-making and the engineering systems that depend upon them.