Numerical Methods for Engineering Design and Optimization (18-660 @ CMU)

  1. Introduction to numerical computation
  2. Ordinary differential equation (ODE)
  3. Partial differential equation (PDE)
  4. Thermal analysis
  5. Linear solver I: Gaussian elimination
  6. Linear solver II: LU decomposition & Cholesky decomposition
  7. Nonlinear solver: Newton-Raphson method & binary search
  8. Linear regression I: least-squares fitting
  9. Over-determined linear system
  10. Convex analysis: convex set, convex function & convex optimization
  11. Linear regression II: regularization
  12. Linear regression III: compressive sensing
  13. Classification: support vector machine (SVM)
  14. Geometric problems
  15. Unconstrained optimization I: golden section search & downhill simplex method
  16. Unconstrained optimization II: gradient method & Newton method
  17. Constrained optimization I: linear equality constraint
  18. Constrained optimization II: interior point method
  19. Constrained optimization III: duality
  20. Conjugate gradient method I: quadratic programming
  21. Conjugate gradient method II: conjugate search direction
  22. Conjugate gradient method III: iterative algorithm
  23. Conjugate gradient method IV: pre-conditioning
  24. Monte Carlo analysis I: random sampling
  25. Monte Carlo analysis II: Latin hypercube sampling & importance sampling
  26. Monte Carlo analysis III: principal component analysis (PCA)
  27. Randomized algorithm I: random walk
  28. Randomized algorithm II: simulated annealing