Lecturer: Jonathan
Korman Office: BA6236 email: jkorman at math at toronto at edu (do not send email to any other accounts) Office Hours: Wed 5:15-6 and Fri 4-4:30 |
Teaching
Assistant:
Mykola Matviichuk Office Hours: Mon 12-1 and Tue 10-11 in BA6135 email: mykola dot matviichuk at mail dot utoronto dot ca |
# | Week of ... | |
Fall Semester: | ||
0 | Sep 8 | Introduction |
1 | Sep 11 | Review. Finite dimentional optimization (unconstrained problems): 1st and 2nd order neccessary conditions for a minimum. |
2 | Sep 18 | Finite dimentional optimization (unconstrained problems): 2nd order sufficient condition for a minimum. Convex functions: C^{ 1 } and C^{ 2 } characterizations. |
3 | Sep 25 | Convex functions: local minimum is a global minimum, maxumum is attained on boundary of compact convex domain. Introduction to Finite dimentional optimization (equality constraints): Lagrange multipliers. |
4 | Oct 2 | Finite dimentional optimization (equality constraints): 1st and 2nd order neccessary conditions for a local minimum. 2nd order sufficient condition for a local minimum. |
5 | Oct 9 | Finite dimentional optimization (inequality constraints): 1st and 2nd order neccessary conditions for a local minimum. 2nd order sufficient condition for a local minimum. |
6 | Oct 16 | Algorithems: Newton's method, method of steepest descent. |
7 | Oct 25 | Midterm. Steepest descent. |
8 | Oct 30 | Conjugate direction methods. Conjugate gradient method. |
Nov 6 | Reading week. | |
9 | Nov 13 | Global convergence theorem. Calculus of Variations: introduction. |
10 | Nov 20 | Calculus of Variations: 1st order necc. conditions, Euler-Lagrange equation. |
11 | Nov 27 | Calculus of Variations: Examples, classical mechanics (least action principle). |
12 | Dec 2-4 | Calculus of Variations: equality constraints, sufficient conditions (convexity). |
Dec 9-20 | Final Exams period |