These notes are from some of my classes and reading in grad school.

  • Robust and stochastic optimization
    — robust, chance-constrained and sampled convex programming
  • Convex analysis
    — convex sets and functions
    — Fenchel, conic and Lagrangian duality
    — algorithms for nonsmooth optimization
    — variational analysis and the KKT conditions
  • Linear programming
    — geometry and duality
    — simplex, ellipsoid and interior point methods
    — extension to conic programming
  • Monte Carlo simulation
    — sample sizes and confidence intervals
    — random number generation
    — variance reduction
    — gradient estimation
  • Model-based estimation
    — batch least-squares estimation
    — the Kalman filter and square-root techniques
    — nonlinear filtering (EKF, UKF, and particle filters)
  • Matrix algebra review
    — norms, factorizations, derivatives and eigenstuff
  • Probability and statistics basics
    — distributions, moments, correlation and covariance, transformations and limit theorems
    — maximum likelihood and Bayesian estimation, hypothesis testing