Research

My research focuses on the modeling, analysis, and optimization of complex socio-technical systems (STS) such as smart power grids, EV charging ecosystems, and sustainable transportation networks. These systems are large-scale, highly interconnected, and uncertain, making classical optimization and purely data-driven methods insufficient on their own.

I work at the intersection of large-scale optimization, stochastic modeling, network science, game theory, and machine learning, with the goal of developing methods that are both theoretically grounded and computationally scalable for real-world implementation over highly interconnected networks.

Solving STS is inherently challenging: these problems combine large-scale optimization over highly interconnected networks with massive datasets, making it difficult to compute high-quality solutions under significant uncertainty. My goal is to leverage machine learning to simplify complex problem structures and build optimization proxies that deliver fast, near-optimal decisions.

EV Infrastructure Planning: Integrating Demand Estimation, Coverage Optimization, and Grid Load Management (ongoing)

We developed a three-phase framework for EV charging infrastructure planning. The first phase focuses on forecasting charging demand using real-time spatial data. The second phase formulates a two-stage stochastic optimization model to determine optimal charger locations and capacities, while the third phase evaluates the power hosting capacity of the underlying grid.

A major challenge is the large-scale and complex network structure of the problem. To address this, we leveraged graph-theoretic techniques to remove redundant edges and reduce network complexity, and incorporated column generation to improve computational efficiency.

To further enhance scalability and demand prediction accuracy, we collaborated with the UT Austin group to develop a data-driven framework based on K-means clustering and Voronoi diagrams. We also proposed a bipartite graph learning approach that delivers near-optimal solutions with significantly reduced computational cost.

Post-disaster Grid Restoration Considering Coupled Transportation-Power Networks (ongoing)

Restoring power after extreme events such as tornadoes or hurricanes is challenging due to uncertain grid damage and disrupted transportation networks, which limit crew mobility. To address this, we developed a two-stage restoration framework on coupled transportation-power networks that minimizes overall service downtime.

Multiple repair crews are modeled as independent agents, enabling decentralized coordination and efficient task allocation. Since conventional exact optimization-based allocation struggles to scale for such large and dynamic systems, we developed a graph reinforcement learning (GRL) framework with bipartite graph matching, in collaboration with the University at Buffalo.

The GRL model learns incentive functions for assigning crews to repair tasks by leveraging the power restoration potential of damaged components and a graph-abstracted representation of system states, achieving scalable and near-optimal restoration policies.

Optimal Designing of Electric Ships for Maritime Decarbonization Under Voyage Uncertainties (completed)

The optimal sizing of small modular reactors (SMRs) and battery energy storage systems within the confined space of ships is critical for improving operational flexibility and reliability. In this work, we developed a stochastic optimization framework for the sizing and scheduling of shipboard SMR-battery energy systems as a clean alternative for marine transportation. The model captures the space-constrained, dynamic maritime operating environment and explicitly accounts for uncertainty in propulsion load demands. We validated the approach on real-world ship case studies. This work was published in IEEE Transactions on Transportation Electrification.

Convergence Rates for Optimization Problems with Variational Inequality Constraints (completed)

We study a broad class of optimization problems with Cartesian variational inequality (CVI) constraints and propose a unified formulation that captures problems with equilibrium constraints, complementarity constraints, and inner-level large-scale optimization structures. These models naturally arise in analyzing the efficiency of equilibria in multi-agent networked systems, such as communication networks and power systems.

To solve this class of problems, we develop a first-order algorithm, termed the averaging randomized block iteratively regularized gradient scheme, and establish non-asymptotic convergence rate guarantees for both suboptimality and infeasibility. To our knowledge, this is the first work providing rate guarantees for this class of CVI-constrained problems. Numerical experiments on networked Cournot competition models demonstrate the effectiveness of the proposed approach in computing efficient Nash equilibria.

Distributed Optimization for Problems with Variational Inequality Constraints (completed)

We study constrained multi-agent optimization problems in which agents cooperatively minimize a global objective while having access only to local objective functions and constraint information. To address this decentralized setting, we propose a unified formulation that captures distributed optimization problems with complementarity constraints, local nonlinear inequality and linear equality constraints, and coupling nonlinear equality constraints.

We develop an iteratively regularized incremental gradient method in which agents communicate over a cycle graph at each iteration. Our analysis establishes non-asymptotic, agent-wise convergence rates for both suboptimality and infeasibility of the associated variational inequality constraints. A key contribution is the introduction of agent-wise averaging, which enables corresponding agent-level convergence guarantees. Numerical experiments on a transportation network equilibrium problem, along with comparisons to existing incremental gradient methods, demonstrate the effectiveness of the proposed approach for constrained finite-sum optimization.

Incremental Gradient Method for Large-scale Distributed Nonlinearly Constrained Optimization (completed)

We study finite-sum optimization problems with hard-to-project constraint sets, where standard incremental gradient (IG) methods suffer from expensive projection steps—particularly in the presence of nonlinear constraints or large numbers of linear constraints.

To overcome this limitation, we develop an averaged iteratively regularized incremental gradient method that eliminates the need for explicit projections. Under mild assumptions, we establish non-asymptotic convergence rates for both suboptimality and constraint infeasibility. Numerical experiments on distributed soft-margin support vector machine problems demonstrate that the proposed approach outperforms standard projected IG methods, highlighting its scalability and practical effectiveness.

Presentation for ACC2021 is available at https://youtu.be/qrYmnRaEZLk

Randomized Block Coordinate Iterative Regularized Subgradient Method for High-dimensional Ill-posed Convex Optimization (completed)

Motivated by ill-posed optimization problems in image processing, we study a bilevel optimization framework in which a secondary objective is minimized over the solution set of an inner-level problem. While classical approaches such as minimal-norm gradients, sequential averaging, and iterative regularization are well known, they struggle with nondifferentiable objectives and high-dimensional decision spaces.

To address these challenges, we develop a randomized block-coordinate iteratively regularized subgradient method. With uniform block sampling and carefully designed stepsize and regularization schedules, we establish convergence guarantees and rate results in terms of the expected inner-level objective value. Numerical experiments on image processing problems demonstrate the effectiveness and scalability of the proposed approach.

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