VIRTUAL HANDOUT for

Nonlinear Programming - C&O 367
Winter 2003

This course provides an introductory treatment of topics in Nonlinear Programming. This includes a hands-on approach with exposure to existing software packages.

Conduct of Course

Instructor:

Professor Henry Wolkowicz, MC 6065, ext. 5589, hwolkowi@orion.math.uwaterloo.ca

Teaching Assistant:

Hua Wei (h3wei@math.uwaterloo.ca)

Office Hours:

Henry Wolkowicz, MC6065: Monday 1-2PM and Friday 10-11AM
Hua Wei (h3wei@math.uwaterloo.ca) MC 5052: Wed. 1-2PM

Lectures:

Tuesday-Thursday, 10-11:20AM, MC 4060.

Text:

The Mathematics of Nonlinear Programming, by Peressini, A.L., Sullivan, F.E., Uhl, J.J.. ( Please send me any typos that you find! )

Home Page, C&O 367, http://orion.math.uwaterloo.ca/~hwolkowi/henry/teaching/w03/367.w03/readme.html

Term Work:

homework problems

midterm (in class) exam

Late assignments will not be accepted.

Midterm Exam:

80 minutes, Thursday Feb. 27, in class.

Final Exam:

Marking Scheme:

Homework 40% (best 6 out of 7 assignments)
Mid-term Exam 20%
Final Exam 40%

COURSE TOPICS OUTLINE - C &O 367
(with HOMEWORK LIST)

Lectures start Tuesday Jan 7, 2003.

Chapter Outlines

Chap.

Start Class Outlines

START HOMEWORK

(solutions are on reserve in the library - call number UWD1927 (call numbers are also available from the library web catalogue))

Homework #0 in html (Revision); due Tuesday January 14 (homework ps file)
- Reading: text Chapter 1, sections 1.1, 1.2.
- References (FYI): NEOS Guide Optimization Tree; FAQ on nonlinear programming.

Optimality Criteria; Quadratic Functions
- HOMEWORK:
  - due: Thursday January 23. (homework ps file) and (homework pdf file)
  - Reading: Text Chapter 1. (finish the chapter, 1.3,1.4,1.5)
  - References (FYI):
    - Eigenvalue Show; this is a matlab file called eigshow.m. This file provides an eigenvalue show that is both entertaining and informative. (Other such files are available.
    - Interior-Point Methods, information, movies, ... at Argonne.
Convex Sets and Functions
- HOMEWORK:
  - due: Tuesday, Feb. 4 (at start of class) (homework ps file) and (homework pdf file)
  - Reading: Text Chapter 2. (chapter, 2.1,2.2,2.3)
  - References (FYI):
    - Introduction to Convex Optimization, course notes by Stephen Boyd, including Lagrangian duality, LP duality, interior-point methods, and semidefinite programming; see also Part 3 in the notes by Lieven Vandenberghe
    - Open Problem from Mathematics Web:
Geometric Programming; and Iterative Methods for Unconstrained Optimization
- HOMEWORK:
  - due: Thursday, Feb. 13 (at start of class)
    - Pg 79-80, Problems: 15a)e). (Note: x,y,z positive is needed in 15 e))
    - Pg 128-9, Problems: 1,3,4,7.
  - Reading: Text Chapter 2. (finish chapter, 2.3,2.4,2.5; and start chapter 3.1,3.2)
  - FYI:
    - See Part 3 in the notes by Lieven Vandenberghe.
Iterative Methods for Unconstrained Optimization
- HOMEWORK:
  - due: Tuesday, Feb. 25, 2003. (at start of class)
    - Pg 128-130, problems: 8, 13, 16, 20.
  - Reading: Text Finish Chapter 3. (chapter, 3.1,3.2,3.3,3.4,3.5)
  - References (FYI):
    - unconstrained optimization, at OTC; see e.g. line search methods
Least Squares Problems .... and Convex Programming
- HOMEWORK:
  - due: Thursday, Mar. 13, 2003 (at start of class)
    - Pg 153, problem 1,7 and Pg 212, problems: 1,2,3.
  - Reading: Text Chapter 4., section 4.1 only. Chapter 5, sections 5.1 and 5.2.
Convex Programming and the Karush-Kuhn-Tucker Conditions cont...
- HOMEWORK:
  - due: Mar. 20, 2003
    - Pg 212-213 Problems 4,5, and for question 5 find the linearizing and tangent cones at an optimum and verify that they are equal; Pg 214 Problem 13
  - Reading: Text Chapter 5. (chapter, 5.1,5.2,5.4)
  - FYI:
    - See Part 4 in the notes by Lieven Vandenberghe.
Convex Programming and the KKT Conditions continued...
- HOMEWORK:
  - due: April 1, 2003 (at start of class)
    - Pg 213, Problem 7; Pg 214, Problems 9,14.

Mail to: hwolkowi@orion.math.uwaterloo.ca
(C) Copyright Henry Wolkowicz, 1991.
, by Henry Wolkowicz