# Math 164 Lecture 1

## 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%

• 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