APM462 - Fall 2017
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
 

General Info



Course Calendar (tentative)

# 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