Math 33A Lecture 1 Fall 2006

Mathematics 164A Lecture 1 - Winter 2007

Optimization

Course homepage: www.math.ucla.edu/~xinweiyu/164.1.06w/index.html.
Time and Place: MWF 10:00am -- 10:50am, PAB 1749.
Discussion Session: R 10:00am -- 10:50am, MS 6221.
Instructor: Xinwei Yu (xinweiyu@math.ucla.edu)
Office hours: MWF 11:00am -- 12:00am at MS 7360.
TA: Yanghong Huang (yhhuang@math.ucla.edu)
Office hours: T 10:00am -- 11:00am, R 11:00am -- 12:00am at MS 7630.
Textbook: Excerpts from “Linear and Nonlinear Programming” by S. Nash and A. Sofer.
Exams:
- Midterm: Monday, Feb. 12, 10:am - 10:50am, PAB 1749.
- Final: Friday, Mar. 23, 2007, 8:00am-11:00am.

Course schedule (subject to change).

Week	M	W	F	Homeworks
1 (01/08-01/12)	Examples of optimization problems	Feasibility & Optimality	Linear Programming: Introduction	HW 1
2 (01/15-01/19)	Martin Luther King Jr. holiday	Linear Programming: Optimality conditions	cont.	HW 2
3 (01/22-01/26)	Linear Programming: general theory	cont.	Standard form of linear programs	HW 3
4 (01/29-02/02)	Simplex method	cont.	Dual problems	HW 4
5 (02/05-02/09)	Duality theory	Complementary slackness & Sensitivity analysis	Midterm review	HW 5
6 (02/12-02/16)	Midterm	Review of midterm (or Game theory)	Unconstrained nonlinear optimization: optimality conditions	HW 6
7 (02/19-02/23)	Presidents’ Day holiday	Unconstrained nonlinear optimization: Newton's method	Linear equality constrained problems: optimality conditions	HW 7
8 (02/26-03/02)	Nonlinear equality constrained problems: optimality conditions	Linear inequality constrained problems: optimality conditions	cont.	HW 8
9 (03/05-03/09)	Nonlinear inequality constrained problems: optimality conditions	The Lagrangian function and sensitivity analysis	Interior point methods	HW 9
10 (03/12-03/16)	Convexity and convex optimization	cont.	Final Review	HW 10

Lecture notes for each topic will be posted after that topic has been covered in class.

Homeworks will be posted at the beginning of each week, and collected in the discussion section the next week. For example, HW1 will be posted no later than Monday 01/08, and will be collected in the discussion section on Thursday 01/18.
Homework 10 will not be collected.

Exams.
- No makeup exams under any circumstances. If you need to take an early final, talk to the instructor before the midterm.
- Both exams (midterm and final) are open book. You can bring whatever reference you need. However when citing existing results, you can only cite those in my online lecture notes, not even the textbook.
- In the exams, you need to write down all the steps that lead to your answer to get full credit. Otherwise you may not receive full credit.
- Please remember to bring a picture ID to all the quizzes and exams and make it visiable. It may be checked.

Grading:
- my.ucla.edu will be used.
- The lowest score among Homeworks 1--9 will be dropped.
- Two schemes will be used.
  1. Homeworks: 20%; Midterm: 40%; Final: 40%.
  2. Homeworks: 20%; Final: 80%.
  The final grade will be the higher one from the two methods.
- The final will cover all the materials. With about 50% points on materials before the midterm, and 50% for materials after the midterm.
- The grade "incomplete" will only be given in very special cases, when a student
  - is doing well in the course, and
  - cannot take the final for a very serious and documented reason, and
  - contacts the instructor before the final.