projects

Research projects on optimization, control, and variational analysis, plus undergraduate research ideas for AMS 487 and prospective students at SUNY Korea.

My research develops the variational analysis, optimal control, and numerical methods for systems with constraints and contact, and applies them to crowds, vehicles, and learning. The undergraduate projects below are entry points into the same ideas.

Research (3) Undergraduate projects (9) How to apply Preparation roadmap

Research ongoing lines of work

Active program

Optimal Control of Sweeping Processes

Discrete approximations, optimality conditions, and applications of Moreau's sweeping process and its controlled variants.

Optimal control · Nonconvex sweeping · Discrete approximation
Papers in J. Differential Equations, DCDS-B, IEEE Control Syst. Lett., JOTA; Nonlinear Anal. Hybrid Syst. (accepted, 2026)
Submitted, 2026

Catching-Up Algorithm for Differential Inclusions

Convergence, stability, and quantitative error bounds for discretizations of differential inclusions driven by maximal monotone operators.

Catching-up algorithm · Maximal monotone operators · Error bounds
Joint work with Hassan Saoud
Applications

Crowd Motion & Marine Vehicle Control

Optimal control of nonconvex sweeping processes applied to pedestrian dynamics, evacuation, and autonomous marine surface vehicles.

Crowd motion · Marine vehicles · Free-time control
With B. S. Mordukhovich, G. Colombo and coauthors

Undergraduate projects AMS 487, independent study, or a first research experience

Intro Control and optimization

Python Toolbox for Optimal Control

Build a small, well-documented Python toolbox that solves classic optimal-control problems (brachistochrone, LQR, simple sweeping process) and visualizes trajectories.

Time: 1 semester
Background: Calculus, basic ODEs, Python
Intro Numerics and dynamics

Bouncing Ball in a Moving Polygon

A first undergraduate research project on projections, constrained motion, and sweeping processes, starting from linear algebra and Python.

Time: 4–6 week trial, then a semester
Background: Multivariable calculus, linear algebra, Python
Core Learning and RL

Reinforcement Learning for Crowd Evacuation

Train an RL agent that learns to evacuate a simulated crowd from a room with obstacles in minimum time — a friendly entry point into RL and nonsmooth dynamics.

Time: 1 semester
Background: Python, probability, linear algebra
Core Control and optimization

Trajectory Planning for a Simulated Boat

Implement and visualize a free-time optimal navigation problem for an autonomous surface vehicle avoiding circular obstacles.

Time: 1 semester
Background: ODEs, Python
Core Learning and RL

Policy Gradient for Mean-Variance Portfolio Optimization

Reproduce a regime-switching financial market and train a policy-gradient agent to balance expected return and variance — a bridge between optimization, finance, and RL.

Time: 4–6 week trial, then a semester
Background: Calculus, linear algebra, probability and statistics, Python
Core Numerics and dynamics

Catching-Up Algorithm — Numerical Experiments

Implement Moreau's catching-up algorithm in Python and experimentally verify the error bounds for several test problems.

Time: ½–1 semester
Background: Numerical analysis, Python
Core Control and optimization

From Lagrange Multipliers to Discrete Pontryagin

Climb the ladder from constrained calculus to optimal control's necessary conditions using only multivariable calculus and a willingness to write down chain rules carefully.

Time: 1 semester
Background: Multivariable calculus, Python
Core Learning and RL

From Gridworld MDP to Crowd Evacuation

Start with the Bellman equation as a linear system on a 5×5 grid and end with a continuous-space multi-agent crowd evacuation simulator — touching every concept that bridges classical dynamic programming to modern reinforcement learning.

Time: 1 semester
Background: Probability, linear algebra, Python
Advanced Learning and RL

Flow Matching — Learning to Turn Noise into Data with ODEs

Build a modern generative model from scratch using nothing but vector fields, ODEs, and a willingness to follow a particle along a straight line. A gentle on-ramp from multivariable calculus to the math behind today's image and robotics generative models.

Time: 1 semester
Background: Multivariable calculus, ODEs, probability, Python

Levels: Intro needs only first-year calculus and linear algebra. Core assumes one or two further courses. Advanced is the most programming- and prerequisite-heavy.

How to apply

Not sure which project fits? Start with an Intro project and a short trial of four to six weeks. Email me (see the contact page) with:

  • your relevant courses in calculus, linear algebra, probability, optimization, and programming;
  • one paragraph on why a project interests you;
  • any prior experience in Python, statistics, or machine learning.

No project requires prior research experience. Curiosity and follow-through matter most. The preparation roadmap lists the courses and skills that help.