MATH 484 - Nonlinear Programming

Schedule

  1. Aug 26 Introduction. Program for apples Chapter 1.1 - self study - Functions of one variable - first derivative and extremes
  2. Aug 28 Chapter 1.2 - definitions of closed,open set, ball, functions of more variables
  3. Aug 30 Chapter 1.2 and 1.3 - quadratic form, semidefinite matrices
  4. Sep 2 Labor day (no class)
  5. Sep 4 Principal minors for deciding if matrix is positive definite HW1 is due
  6. Sep 6 Coercive functions
  7. Sep 9 Eigenvalues and positive (semi)definite matrices
  8. Sep 11 Convex sets HW2 is due
  9. Sep 13 Convex functions
  10. Sep 16 Convex functions and AG inequality
  11. Sep 18 applications of AG inequality HW3 is due
  12. Sep 20 Geometric program and its dual
  13. Sep 23 Examples of solving geometric programs
  14. Sep 25 Properties of closest point in a convex set. Chapter 5.1 HW4 is due
  15. Midterm time Sep 26, 145 AH from 6-9 pm
  16. Sep 27 Uniqueness and existence of closest point
  17. Sep 30 Separation and support theorem
  18. Oct 2 Definitions for general programs HW5 is due
  19. Oct 4 Linear programming applications
  20. Oct 7 More applications of linear programming Program 1 Program 2
  21. Oct 9 Farkas lemma and MP(z) HW6 is due
  22. Oct 11 MP and sensitivity vector
  23. Oct 14 KKT theorem - statement and first part of proof
  24. Oct 16 KKT theorem - finished proof, gradient version, example of usage HW7 is due
  25. Oct 18 extended AG inequality
  26. Oct 21 example of usage of extended AG on geometric program
  27. Oct 23 dual geometric program HW8 is due
    Program form the class: maximize (2/r)^r * (1/(-4+4r))^(-2+2r) * (1/(4-2r))^(1-r/2) * (1/(-1+2r))^(-1/2+r) * (-2+3r)^(-2+3r) * (0.5+0.5*r)^(0.5+0.5*r) where 1 <= r <= 2
  28. Oct 25 duality of geometric program and duality for everyone
  29. Oct 28 duality for everyone - in particular for linear programming
  30. Oct 30 penalty method - introduction HW9 is due
  31. Midterm time Oct 31, 145 AH from 6-9 pm
  32. Nov 1 penalty method - applications
  33. Nov 4 absolute value penatly methods
  34. Nov 6 coercive funcitons and duality gap
  35. Nov 8 Newton's method. Chapter 3.1
  36. Nov 11 Newton's method and steepest descent method, Chapter 3.1 and 3.2
  37. Nov 13 Steepest descent method and Wolfes theorem, Chapter 3.2 and 3.3 HW 10 is due
  38. Nov 15 Sage, steepest descent and Broyden's method, Chapter 3.3 and 3.4
  39. Nov 18 Broyden's method 3.4
  40. Nov 20 BFGS and DFP HW 11 is due
  41. Nov 22 NO CLASS
  42. Nov 25 Thanksgiving (no class)
  43. Nov 27 Thanksgiving (no class)
  44. Nov 29 Thanksgiving (no class)
  45. Dec 2 Interior point methods
  46. Dec 4 NO CLASS
  47. Midterm time Dec 5, 145 AH from 6-9 pm
  48. Dec 6 NO CLASS
  49. Dec 9 Semidefinite programming - only first 12 pages
  50. Dec 11 Semidefinite programming
  51. Dec 20 8:00-11:00 AM FINAL EXAM - 345 Altgeld Hall