Optimization

Optimization is concerned with the analysis and algorithmic aspects of maximizing or minimizing an objective function subject to constraints, often in complex problems in high dimension. Active research areas in ORFE include interior-point methods, the parametric simplex method, stochastic optimization, and convex analysis. Applications of interest span from portfolio optimization to engineering applications such as optimal control, optical design, and machine learning.

Research Area Faculty and Interests

  • aaa's picture
    Research Interests:
    Development of computational tools for optimization of sociotechnical systems arising in operations research and engineering, algebraic methods in optimization, semidefinite programming, polynomial optimization, dynamical systems and control, Lyapunov methods for stability and robustness verification, computational complexity in optimization, convex relaxations in combinatorial optimization, and applications of these tools to semialgebraic problems in statistics, economics, and systems theory.
  • alaink's picture
    Research Interests:
    Autonomous Vehicles, SmartDrivingCars, the fundamental design of computer vision techniques for for the rapid classification and identification of the driving environment, analysis and classification of collision-free driving scenarios, quantification of accident risk and the investigation, formulation and design of, pay-as-the-car-drives, Investigation and creative design of the human-computer interfaces for SmartDrivingCars, operational and feasibility analyses of autonomousTaxi (aTaxi) systems
  • mulvey's picture
    Research Interests:
    Financial optimization models and associated algorithms, asset management strategies for global pension plans, (re)insurance companies, and other long-term investors, dynamic portfolio tactics for hedge funds, replicating performance of active managers
  • bs37's picture
    Research Interests:
    Data-driven computational tools for mathematical optimization, machine learning and optimal control. Real-time and embedded optimization. Dynamical systems and optimization-based control. Differentiable optimization. First-order methods for large scale optimization. Machine learning for optimization and data-driven algorithms. Applications include control of fast dynamical systems, finance, robotics and autonomous systems.
  • rvdb's picture
    Research Interests:
    Interior-point methods for linear, convex, nonconvex, semidefinite optimization, robust optimization, the parametric simplex method, and constraint matrix sparsification (e.g. fast Fourier optimization). Applications include high-contrast imaging (to design a NASA space telescope), finding new stable periodic solutions to the n-body problem, Machine Learning, portfolio selection, option pricing, and least-absolute-deviation statistics. Related side activities include algorithms to address grade inflation, quantifying climate change, and making Purple America maps.