MATH 484 - Nonlinear Programming

Schedule

  1. Aug 27 Introduction. Chapter 1.1 - Functions of one variable - first derivative and extremes
  2. Aug 29 second derivative as an indicator for min/max, Chapter 1.2 - bunch on definitions
  3. Aug 31 analogs for function of more variables, quadratic form, postitive semidefinite matrix, Chapter 1.2 - other part
  4. Sep 3 Labor day (no class)
  5. Sep 5 semidefinite matrices, determinant criterium, Chapter 1.3 HW 1 is due
  6. Sep 7 coercive functions, eigen values as criterum for semidefinite matrix , Chapter 1.3, 1.4
  7. Sep 10 Convex sets, Chapter 2.1
  8. Sep 12 Convex functions, Chapter 2.3 HW 2 is due
  9. Sep 14 A-G inequality, proof and examplem, Chapter 2.4
  10. Sep 17 A-G inequality, definition od geometric programming, Chapter 2.4
  11. Sep 19 Geometric programming, Chapter 2.5 HW 3 is due
  12. Sep 21 Least squares - theory, Chapter 4.1
  13. Sep 24 Least squares for a line, Chapter 4.1
  14. Sep 26 QR-factorization, Chapter 4.1 HW 4 is due
  15. Midterm time Sep 27 6pm - 170 Everitt Lab - Chapters 1 and 2
  16. Sep 28 Projection and underdetermined system of equations Chapter 4.2 and Chapter 4.3
  17. Oct 1 Midterm review, generalized norms Chapter 4.4
  18. Oct 3 Separation and support theorems, Chapter 5.1
  19. Oct 5 Separation and support theorems, Chapter 5.1
  20. Oct 8 definitions of convex program, Chapter 5.2. Linar programming examples
  21. Oct 10 Linar programming examples HW 5 is due
  22. Oct 12 Definition of MP(z), Chapter 5.2
  23. Oct 15 examples for MP(z) sensitivity vector, definition of Lagrangian, Chapter 5.2
  24. Oct 17 Karush-Kuhn-Tucker theorem, Chapter 5.2 HW 6 is due
  25. Oct 19 Usage of KKT, extended AG inequality, Chapter 5.2 and 5.3
  26. Oct 22 Constrained geometric programming, Chapter 5.3
  27. Oct 24 Duality on constrained geometric programming, Chapter 5.3 HW 7 is due
  28. Oct 26 Dual convex programs and demonstration on linear programming, Chapter 5.4
  29. Oct 29 Duality gap for convex programs, Chapter 5.4
  30. Oct 31 Penalty method, Chapter 6.1 HW 8 is due
  31. Midterm time Nov 1 6pm - 143 Altgeld Hall
  32. Nov 2 Penatly method, Chapter 6.2
  33. Nov 5 Penatly method, Chapter 6.3
  34. Nov 7 Newton's method for unconstrained optimization, Chapter 3.1
  35. Nov 9 Method of steepest descent, Chapter 3.2
  36. Nov 12 Designing better method, Chapter 3.3
  37. Nov 14 Trust region method and Broyden's method, Chapter 5.5 and Chapter 3.4HW 9 is due
  38. Nov 16 NO CLASS
  39. Nov 19 Thanksgiving (no class)
  40. Nov 21 Thanksgiving (no class)
  41. Nov 23 Thanksgiving (no class)
  42. Nov 26 Broyden's method and preparation for BFGS, Chapter 3.4 and Chapter 3.5
  43. Nov 28 BFGS and DFP, Chapter 3.5
  44. Nov 30 NO CLASS
  45. Dec 3 Semidefinite programming - introduction, same as linear programming
  46. Dec 5 Semidefinite programming - quadratic contraints HW 10 is due
  47. Midterm time Dec 6 6pm - 143 Altgeld Hall
  48. Dec 7 Semidefinite programming - MaxCut algorithm using semidefinite programming
  49. Dec 10 Interior point method - theoretical concept and main idea
  50. Dec 12 NO CLASS
  51. Dec 17 8:00-11:00 AM FINAL EXAM - 443 Altgeld Hall