AMAT 425 L01 (Fall 2007)
"Introduction to Optimization"
Course Outline
Instructor:
Anatoliy Swishchuk
E-mail: aswish@ucalgary.ca
Office: MS552
Tel.: (403) 220-3274
Office Hours: TR:11:00am-11:50am

Place:
Lectures Schedule and Tutorials for  AMAT 425
Lectures schedule (L01)
Tutorials  schedule (T01)
Monday/Wednesday/Friday: 14:00-14:50  (CHE202)
 Tuesday: 12pm-12:50pm (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, quasi-newton
Least Squares: least squares fit, minimum norm solutions
Linear Programming: simplex method, primal-dual 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, 12:00-12:50 (MS515)
  Quiz # 2: Oct 16, Tue, 12:00-12:50 (MS515)
Midterm: October 29, Mon, 14:00-14:50 (CHE202)
Quiz # 3: Nov 6, Tue, 12:00-12:50 (MS515)
  Quiz # 4: Nov 27,  Tue, 12:00-12:50 (MS515)
  Last day of class: December 7, Fri, 2007.
 
Final Exam:
Wed, December 19, 3:30-5:30pm, 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 Listing-Undergraduate (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 web-page). The address of this web page is: http://www.math.ucalgary.ca/~aswish/amat425F07.html/

Class work:
In-class lectures with typical examples (lecture notes will be posted on the webpage in the form of pdf-files
);
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, 3:30-5:30pm, 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: Quasi-Newton 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
Oct-Nov
29
Midterm 1
Lec21: The Method of Least Squares: Short Intro and Some Examples 2
Lec22: Least Squares Analysis: Miinimizing ||Ax-b||^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, Primal-Dual Method   23
Lec30: Linear Programming: The SOB Method and Revised Simplex Method
Nov
26
Lec31: Linear Programming: The Revised SM-Overall 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.