APM462, Winter 2018


APM462 - Winter 2018
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

General Info

Lectures: Mon 6-9pm in LM 162
Office hours begin the week of Jan 15.
The suggested textbook for this course is Linear and Non-Linear Programming (4th Edition) by David Luenberger & Yinyu Ye. Publisher: Springer. Should be available at the UT bookstore. The textbook is suggested and not required: I will try to make the lectures and HW self contained.

Before classes begin, I suggest reviewing some multivariable calculus, especially the part about partial derivatives, gradients, Taylor expansion, and the Jacobian matrix. Refreshing basic linear algebra would also be helpful.

Course Syllabus (approximate):

Linear and Non-Linear Programming: parts of chapters 7,8,9,11.
The Calculus of Variations.
Supplementary material from lectures.

The Course Grade will be calculated as follows:

20% Homework
30% Term Test
50% Final Exam

There will be 5 or 6 homework assignments. Assignments are to be handed in on assigned dates at the beginning of class.
Please staple your homeworks. Unstapled homeworks will be penalized 2 points.
NO late homework will be accepted.
Important: There will be no make up term test! If you have a valid reason for missing the term test, the corresponding portion of the final exam will count as your term test grade.

Exam dates:

Term Test: Mon, Feb 26.
Final Exam: Mon, Apr 30, 9am-12.

Please read the information in the two links below about academic misconduct: Plagiarism, Misconduct.
For more information about this course please see Blackboard.

Course Calendar (tentative)

# 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: C¹ and C² 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

#	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: C¹ and C² 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