Skip to content
Nydus Open Learning

Mathematics

Mathematics · Advanced · Level 2

Mathematical optimization

Formulating a model — decision variables, an objective, constraints, and the four things a feasible region can turn out to be; convexity and why it, rather than linearity, is the dividing line; optimality conditions from stationarity through Lagrange multipliers to the KKT conditions and duality; the continuous methods (gradient descent, line search and trust regions, Newton, quasi-Newton, the simplex idea geometrically, interior point, quadratic programming); integer programming with relaxation, branch and bound, cutting planes, network flows and honest heuristics; and optimization under uncertainty — multiple objectives, sensitivity, stochastic and robust formulations, and what a model is and is not.

Ages 18+ 30 lessons about 11 hours in all

Create an account to start Review foundations

You can start now whatever you have done before. Nothing on this page has to be finished first. You can pause anytime; your progress saves automatically.

The lessons

Any lesson can be opened now, in any order. The plan recommends one; it does not lock the rest.

  1. 1 What optimization is, and when it is worth doing
  2. 2 Decision variables, objective and constraints
  3. 3 The feasible region and its four outcomes
  4. 4 Indexed models and summation
  5. 5 When the answer must be a whole number
  6. 6 Reading a model back
  7. 7 Convex sets
  8. 8 Convex functions
  9. 9 Why convexity is the dividing line
  10. 10 Unconstrained optimality
  11. 11 Lagrange multipliers, revisited
  12. 12 The KKT conditions
  13. 13 Duality
  14. 14 Gradient descent
  15. 15 Line search and trust regions
  16. 16 Newton's method for optimization
  17. 17 Quasi-Newton methods
  18. 18 Linear programming geometrically
  19. 19 Interior point methods
  20. 20 Quadratic programming and least squares
  21. 21 Modelling with binary variables
  22. 22 Relaxation and bounds
  23. 23 Branch and bound
  24. 24 Cutting planes
  25. 25 Network flows and the problems that are easy
  26. 26 Heuristics and metaheuristics
  27. 27 Multi-objective optimization
  28. 28 Sensitivity analysis
  29. 29 Stochastic and robust optimization
  30. 30 What a model is and is not