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