Lecturer: Jonathan
Korman Office: HU1024 email: jkorman at math at toronto at edu (do not send email to any other accounts) Office Hour: Th 5-6pm |
Teaching
Assistant:
Mykola Matviichuk Office Hours: Tue and Thr at 10-11am in BA6135 email: mykola dot matviichuk at mail dot utoronto dot ca Andrew Colinet Office Hours: Fri 2-4pm in PG207 email: andrew dot colinet at mail dot utoronto dot ca |
# | Week of ... | |
Winter Semester: | ||
1 | Jan 8 | Review. Finite dimentional optimization (unconstrained problems): 1st and 2nd order neccessary conditions for a minimum. |
2 | Jan 15 | Finite dimentional optimization (unconstrained problems): 2nd order sufficient condition for a minimum. Convex functions: C^{ 1 } and C^{ 2 } characterizations. |
3 | Jan 22 | 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 | Jan 29 | Finite dimentional optimization (equality constraints): 1st and 2nd order neccessary conditions for a local minimum. 2nd order sufficient condition for a local minimum. |
5 | Feb 5 | Finite dimentional optimization (inequality constraints): 1st and 2nd order neccessary conditions for a local minimum. 2nd order sufficient condition for a local minimum. |
6 | Feb 12 | Algorithems: Newton's method, method of steepest descent. |
Feb 19 | Reading Week | |
7 | Feb 26 | Midterm. Steepest descent. |
8 | Mar 1 | Conjugate direction methods. Conjugate gradient method. |
9 | Mar 8 | Global convergence theorem. Calculus of Variations: introduction. |
10 | Mar 15 | Calculus of Variations: 1st order necc. conditions, Euler-Lagrange equation. |
11 | Mar 22 | Calculus of Variations: Examples, classical mechanics (least action principle). |
12 | Mar 29 | Calculus of Variations: equality constraints, sufficient conditions (convexity). |
Apr 9-30 | Final Exams period |