APM462, Spring-Summer 2017


APM462 - Spring-Summer 2017
Lecturer: Jonathan Korman Office: BA6236 email: jkorman at math at toronto at edu (do not send email to any other accounts) Office Hours: Thr 5-6pm in BA6236 and Tue 8-8:30pm in classroom.		Teaching Assistant: Tomas Kojar Office Hours: Tue 5-6pm in BA6180 email: tomas dot kojar at mail dot utoronto dot ca

General Info

Lectures: Tuesday 6-8pm and Thursday 6-7pm in BA B024.
Office hours begin 2nd week of classes.
The suggested textbook for this course is Linear and Non-Linear Programming (4th Edition) by David Luenberger & Yinyu Ye. Publisher: Springer. Should be availlable 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:

25% Homework
30% Term Test
45% 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: Tue, July 4, 6-8pm.
Final Exam: Thr, Aug 17, 7-10pm.

Please read the information in the two links below about academic misconduct: Plagiarism, Misconduct.

Course Calendar (tentative)

# Week of ...

Summer Semester:

1 May 16 Review. Finite dimentional optimization (unconstrained problems): 1st and 2nd order neccessary conditions for a minimum.

2 May 23 Finite dimentional optimization (unconstrained problems): 2nd order sufficient condition for a minimum. Convex functions: C¹ and C² characterizations.

3 May 30 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 June 6 Finite dimentional optimization (equality constraints): 1st and 2nd order neccessary conditions for a local minimum. 2nd order sufficient condition for a local minimum.

5 June 13 Finite dimentional optimization (inequality constraints): 1st and 2nd order neccessary conditions for a local minimum. 2nd order sufficient condition for a local minimum.

6 June 20 Algorithems: Newton's method, method of steepest descent.

7 June 27 Summer break.

8 July 4 Midterm. Steepest descent.

9 July 11 Conjugate direction methods. Conjugate gradient method.

10 July 18 Global convergence theorem. Calculus of Variations: introduction.

11 July 25 Calculus of Variations: 1st order necc. conditions, Euler-Lagrange equation.

12 Aug 1 Calculus of Variations: Examples, classical mechanics (least action principle).

13 Aug 8 Calculus of Variations: equality constraints, sufficient conditions (convexity).

Aug Final Exam.

#	Week of ...
Summer Semester:
1	May 16	Review. Finite dimentional optimization (unconstrained problems): 1st and 2nd order neccessary conditions for a minimum.
2	May 23	Finite dimentional optimization (unconstrained problems): 2nd order sufficient condition for a minimum. Convex functions: C¹ and C² characterizations.
3	May 30	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	June 6	Finite dimentional optimization (equality constraints): 1st and 2nd order neccessary conditions for a local minimum. 2nd order sufficient condition for a local minimum.
5	June 13	Finite dimentional optimization (inequality constraints): 1st and 2nd order neccessary conditions for a local minimum. 2nd order sufficient condition for a local minimum.
6	June 20	Algorithems: Newton's method, method of steepest descent.
7	June 27	Summer break.
8	July 4	Midterm. Steepest descent.
9	July 11	Conjugate direction methods. Conjugate gradient method.
10	July 18	Global convergence theorem. Calculus of Variations: introduction.
11	July 25	Calculus of Variations: 1st order necc. conditions, Euler-Lagrange equation.
12	Aug 1	Calculus of Variations: Examples, classical mechanics (least action principle).
13	Aug 8	Calculus of Variations: equality constraints, sufficient conditions (convexity).
	Aug	Final Exam.