AMAT
425
L01 (Fall 2007)
"Introduction to
Optimization"
Course Outline
Instructor:
Anatoliy Swishchuk
Email: aswish@ucalgary.ca
Office: MS552
Tel.: (403) 2203274
Office Hours: TR:11:00am11:50am
Place:
Lectures
Schedule and Tutorials for AMAT 425
Lectures schedule (L01)

Tutorials schedule (T01)

Monday/Wednesday/Friday:
14:0014:50
(CHE202)

Tuesday: 12pm12:50pm (MS515)

Syllabus:
Unconstrained Optimization: one variable, several variables
Convex Optimization: convex sets and convex functions optimal
conditions, geometric programming
Introductory Numerical Methods: 1D searches, Newton's method, steepest
descent
Practical Numerical Methods: conjugate gradient, quasinewton
Least Squares: least squares fit, minimum norm solutions
Linear Programming: simplex method, primaldual method
Constrained Optimization: penalty methods, Lagrange multipliers
Course
Information Sheet
Important Class Dates:
First day of class: 14:00, Monday,
September 10, 2007
Quiz # 1: Oct 2, Tue, 12:0012:50 (MS515)
Quiz # 2: Oct
16, Tue, 12:0012:50 (MS515)
Midterm: October 29, Mon,
14:0014:50 (CHE202)
Quiz # 3: Nov 6, Tue,
12:0012:50 (MS515)
Quiz # 4: Nov
27, Tue, 12:0012:50 (MS515)
Last day of class: December 7, Fri, 2007.
Final Exam:
Wed, December 19, 3:305:30pm, ST 057
Recommended textbooks:
'Numerical Optimization' by Nosedal J. and Wright S., 2006,
Springer
'An Introduction to Optimization' by E. Chong and S. Zak, 2001, Wiley
Course
Web Page:
The current official syllabus for this course is available in the wall
pockets
across from MS 476 and
on the webpage at www.math.ucalgary.ca
Course ListingUndergraduate (http://math.ucalgary.ca/courses/f07).
There is also a web page for this course which contains the
course
outline, tentative course schedule, grading scheme, important
class dates, etc.
Announcements made in class will be posted there (see end of this
webpage). The address of this web page is:
http://www.math.ucalgary.ca/~aswish/amat425F07.html/
Class
work:
Inclass lectures with typical examples (lecture notes will be posted
on
the webpage in the form of pdffiles);
your computer must have an Adobe Acrobat reader (for free downloading
see www.adobe.com).
Midterm
and Quizzes:
There will be 1 Midterm ( October 27, 2007) and 4 Quizzes
Final
Exam:
Covers all the materials in this course.
Grading
scheme (Course Evaluation) for AMAT425:
Exam, Midterm and Assignments

Value (% of your final mark)

Dates

Midterm

30%

Oct 29

Quizzes (4)

20%=4x5%
(5% for each quiz)

Oct 2, Oct 16, Nov 6, Nov 27

Final Exam 
50% 
Wed, December 19,
3:305:30pm, ST 057

Tentative
Lectures Schedule
for AMAT425
Month

Day

Monday

Day

Wednesday

Day

Friday

Sept

10

Lec1:
Introduction to
Optimization: Mathematical Formulation and
Examples. Course Outline.

12

Lec2:
Unconstrained Optimization: One Variable.

14

Lec3:
Unconstrained Optimization: Two Variables. 
Sept

17

Lec4:
Unconstrained Optimization:
Three Variables.

19

Lec5:
Unconstrained Optimization:
Several Variables I

21

Lec6:
Unconstrained Optimization:
Taylor Expansion and Quadratic Forms

Sept

24

Lec7:
Introductory
Numerical Methods: 1D
Unconstrained Optimization, Overview of Methods. Golden Section
Search 
26

Lec8:
Introductory Numerical Methods: 1D Unconstrained Optimization, Newton's
Method 
28

Lec9:
Introductory Numerical
Methods: 1D Unconstrained
Optimization; Secant Method and Newton's Method in Several Variables

Oct

1

Lec10:
Introductory Numerical
Methods: Steepest Ascent (Descent) 
3

Lec11:
Introductory Numerical
Methods: Steepest
Descent 
5

Lec12:Practical Numerical Methods: Conjugate
Gradient Mehtod 
Oct

8

Thanksgiving
Day (No Lectures)

10

Lec13:
Practical Numerical Methods:
QuasiNewton Method 
12

Lec14:
Numerical Method in
Optimization: Review 
Oct

15

Lec15:
Convex Optimization: Short Intro and Convex Sets.

17

Lec16:
Convex Optimization: Convex
Functions

19

Lec17:
Convex Optimization:
Characterization of Differentiable Convex Functions 
Oct

22

Lec18: Convex Optimization Problems:
Local and Global Minimizers 
24

Lec19: Convex Optimization Problems
(Global Minimizer for Convex Function) and Geometric Programming

6

Lec20:
Convex Optimization Problems:
Review 
OctNov

29

Midterm 
1

Lec21:
The Method
of Least
Squares: Short Intro and Some Examples 
2

Lec22: Least
Squares Analysis: Miinimizing Axb^2 
ov

5

Lec23:
The Method of Least Squares: Minimum Norm Solution 
7

Lec24:
Linear Programming: Intro
and Overview of
Methods 
9

Lec25:
Solving LP Problems: The
Simplex Method (SM) (Geometric Interpretation) 
Nov

12

Reading
Day (No Lectures)

14

Lec26:
Linear Programming: Setting
Up the SM

16

Lec27: Linear Programming: The Algebra of
the SM 
Nov

19

Lec28:
Linear Programming: SM in Tabular Form 
21

Lec29:
Linear Programming: Duality Theory, PrimalDual Method 
23

Lec30: Linear
Programming: The SOB Method and Revised Simplex Method

Nov

26

Lec31:
Linear Programming: The
Revised SMOverall Procedure.

28

Lec32:
Constrained
Optimization: Short Intro and Overview of Methods . Problems with
Equality Constraints. 
30

Lec33:
Constrained
Optimization: Problems with Inequality Constraints

Dec

2

Lec34:
Constrained Optimization:
Lagrange Multipliers,
Examples 
4

Lec35:
Constrained
Optimization:Penalty Methods

6

Lec36:
Constrained Optimization: Penalty Methods II. Course
Review. 
Announcements:
This page was updated on December 27th, 2007.