# Math 164 Lecture 1

## Winter 2015

## Optimization

Lecture Meeting Time: MWF 2:00pm-2:50pm

Lecture Location: MS 5127

**Instructor:**
Luminita Vese

Office: MS 7620 D

Office hours: Mon and Wed at 4pm.

E-mail: lvese[AT]math[DOT]ucla[DOT]edu

Class Web Page: http://www.math.ucla.edu/~lvese/164.1.15w/

__Discussion Section Information__

Time and Location: Thursday 2:00pm-2:50pm, MS 5127.

Teaching Assistant: Zhimin Peng

T.A. E-mail: zhimin.peng[AT]math[DOT]ucla[DOT]edu

T.A. office hours: Tuesday 4pm - 5pm and Thursday 3pm - 4pm.

T.A. office: MS 7630.

**Textbook:** Linear and Nonlinear Optimization (second edition) by I. Griva, S. Nash and A. Sofer.

Or: S. Nash and A. Sofer, *Linear and Nonlinear Programming*, McGraw-Hill. (the older edition).

**Other recommended references:**S. Boyd and L. Vandenberghe, *Convex Optimization*, Cambridge University Press 2004
online version.
P.E. Gill, W. Murray and M.H. Wright, *Practical Optimization*, Academic Press Limited 1981.
J. Nocedal, S.J. Wright, *Numerical Optimization*, Springer Verlag.

**Requisite:** course Math 115A.

**Course Description:**
Fundamentals of optimization. Linear programming: basic solutions, simplex method, duality theory. Unconstrained optimization, Newton's method for minimization. Nonlinear programming, optimality conditions for constrained problems. Additional topics from linear and nonlinear programming.

General Course Information and Outline

**Homework Policy:** Homework will be assigned every week and will be collected the following week on Friday. No late homework will be accepted.

The lowest homework grade will be dropped and will not count for the final grade.

You are encouraged to solve as many problems as you can from the textbook, and not only those from the homework assignments.

There will be theoretical and some computational assignments. For the computational assignments, you can open a computer account and work at the PIC Lab.
Include with your homework the code of the computational assignment used to produce the results and explanations.

**Examinations:**
One midterm exam and one final exam. The examinations are closed-book and closed-note.
No exams at a time other than the designated ones will be allowed (exceptions for illness with document proof, or emergency).

__Midterm:__ Friday, February 20, in class.

- Sample midterm questions [1]
[2]
(solutions posted below in **Handouts:**)

- Sections covered for the midterm: 1, 2.2-2.3 (except 2.3.1), 3.1, 3.2, 4.1-4.4, 5.2, 6.1-6.2.

__Final Exam:__ Final Examination Code: 07 - Friday, March 20, 2015, 3:00pm-6:00pm.

- Sample problems for the final exam (thanks to Prof. Robert Brown):
page [1]
page [2]
page [3]

- Solutions to the sample final problems:
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]

**Grading Policy:** Hw 25%, Midterm 25%, Final 50%

**Useful Links:**
PIC Lab: Boelter Hall 2817
http://www.pic.ucla.edu/piclab/
MATLAB Documentation (thanks to Prof. C. Anderson, UCLA)
Numerical Recipes (see in particular Chapters 10 and 15 from the Numerical Recipes).
Getting started with MATLAB
UCLA problem of the week

**Handouts:**

Example from the lecture on the simplex method

General form of the simplex method
(thanks to Prof. Andrea Brose).

Sample midterm questions [1]
[2]
(thanks to Prof. Robert Brown)

Sample midterm solutions
[1]
[1]
[2]
[3](a,b)
[3](c)
[4](a,b)
[5](a)
[5](b)
[5](c)

Midterm solutions:
Midterm solutions

Sample problems for the final exam (thanks to Prof. Robert Brown):
page [1]
page [2]
page [3]

- Solutions to the sample final problems:
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
Summary of sufficient conditions for local minimizers for non-linear
optimization Summary
Some comments on exercises from the last two homeworks:

Exercise from HW #9

Comments on some exercises from HWs #8 and 9

** Weekly Homework Assignments: **

**HW #1:** due on Friday, January 16

HW1.pdf

**HW #2:** due on Friday, January 23

HW2.pdf

**HW #3:** due on Friday, January 30

HW3.pdf

**HW #4:** due on Friday, February 6

HW4.pdf

**HW #5:** due on Friday, February 13

HW5.pdf

**HW #6:** due on Friday, February 20

HW6.pdf

**HW #7:** due on Friday, February 27

HW7.pdf

**HW #8:** due on Friday, March 6

HW8.pdf

**HW #9:** due on Friday, March 13

HW9.pdf